When Biogen Inc.’s Aduhelm was approved in June, patient advocates hailed the first new Alzheimer’s disease drug in nearly two decades. But health-policy analysts warned that the costly medication would add tens of billions of dollars to Medicare spending even if it were prescribed to just a fraction of people with the memory-loss disease.

Three months later, Aduhelm’s launch has made more of a whisper than a bang. Few patients are being treated with Aduhelm, doctors say, because health insurers are reluctant to pay for a medicine whose effectiveness is hotly disputed among doctors.

Many Alzheimer’s clinics are holding off on prescribing Aduhelm until federal officials decide next year if Medicare will pay for it. Hospitals that do provide the medication often require patients to cover its cost if their insurance refuses to pay; those who can’t are often put on waiting lists.

“Because of the uncertainty, it puts us in limbo,” said Stephen Salloway, director of Butler Hospital’s Memory and Aging Program in Providence, R.I. “The main issue right now is coverage.”

Patients from around the country have been referred to his clinic by doctors whose hospitals aren’t yet providing Aduhelm. Next week, Butler will treat its 10th patient with Aduhelm, Dr. Salloway said, but more than 100 patients have opted to be placed on a waiting list.

“That’s not the way I want to go about this, that only people with means can access the drug,” said Dr. Salloway, who has worked for Biogen as a paid consultant and speaker. “That’s not what the FDA intended. It isn’t equitable.”

Biogen has said the drug, which a doctor or nurse gives by infusion once a month, will cost about $56,000 annually for the average patient. Some estimates peg the price even higher.

Epic Systems Corp., an electronic health records provider, said in an email that fewer than 10 patients were recorded since June 1 as being treated with Aduhelm in its database of anonymized medical records. The database covers more than 116 million patients across 705 hospitals and more than 12,000 clinics.

Among 74 neurologists surveyed by Piper Sandler analyst Christopher Raymond, only two had prescribed Aduhelm as of August. About a third of the doctors said they expect to prescribe the drug within the next six months, and more than half said they expected to do so in the next year, Mr. Raymond said in a note to clients on Aug. 25. Roughly three in five of the neurologists said insurers greatly restrict access to Aduhelm.

Biogen has said that Aduhelm will cost about $56,000 annually for the average patient.

Photo: Adam Glanzman/Bloomberg News

A Biogen spokeswoman declined to comment. Last month, the company said Alzheimer’s specialists are eager to start prescribing the medication, though many are still working to create protocols and infrastructure to manage the treatment of patients.

Wider uptake of the drug hinges in large part on whether Medicare will pay for it and for which patients. The Centers for Medicare and Medicaid Services, or CMS, launched a payment review in July, and expects to issue a proposed policy by January 2022 and a final policy by April 2022.

Biogen has said it expects Medicare, the health insurance program for elderly and disabled people, to cover about 80% of the roughly one million to two million U.S. Alzheimer’s patients who could benefit from the drug.

Aduhelm is approved to treat early-stage Alzheimer’s by removing a sticky protein in the brain called amyloid.

The Food and Drug Administration’s approval of Aduhelm has been controversial because of uncertainty over whether it provides a meaningful benefit to patients and its potential side effects, which include bleeding in the brain. Two large studies of the drug yielded conflicting results, with one showing Aduhelm slowed cognitive decline and the other failing to do so.

Uncertainty about Medicare reimbursement had led some large health insurers, including UnitedHealth Group Inc. and Humana Inc., to hold off on their own coverage policies for commercially insured patients. Others, including the Department of Veterans Affairs and several regional Blue Cross Blue Shield companies, have excluded Aduhelm from their lists of regularly available treatments.

“ ‘We still have concerns about the conflicting data on the safety and efficacy of the drug.’ ”

— A Humana spokesman

Humana is covering the drug for commercial and Medicare-insured patients whose doctors provide paperwork showing they meet the criteria Biogen used to recruit subjects for its clinical trials, a company spokesman said.

“Like many physicians and healthcare delivery systems, we still have concerns about the conflicting data on the safety and efficacy of the drug,” the spokesman said. “Additional guidance from CMS on the coverage policy in the Medicare program is essential and will influence our final coverage determination.”

For now, regional Medicare administrators decide whether to pay for Aduhelm on a case-by-case basis, and so far have received a small number of claims, a CMS spokeswoman said.

Because of the way doctor-administered drugs are paid for, hospitals assume financial risk when they administer medicines like Aduhelm. Under a so-called “buy and bill” system, hospitals and infusion centers purchase drugs like Aduhelm up front from wholesalers and get paid back—along with a small profit—only after infusing a patient with the medication and submitting a reimbursement claim to their insurance plan. If the insurer refuses to pay, the hospital has to seek payment from the patient—or otherwise assume the cost.

“This is where a lot of the fear comes from…in the centers where they want to know, are we going to be reimbursed?” Alisha Alaimo, president of Biogen’s U.S. commercial operations, said in July on the company’s second-quarter earnings call. “And the answer to that is, you’re not going to know until you try.”

A few hospitals, including Cleveland Clinic and Mount Sinai in New York, have said they won’t provide Aduhelm.

Doctors with Montefiore Health System, based in Bronx, N.Y., haven’t begun prescribing Aduhelm yet. A committee of experts from different specialties are developing protocols for using the drug and waiting for clarity on Medicare reimbursement, said Jessica Zwerling, director of the Montefiore Hudson Valley Center of Excellence for Alzheimer’s disease.

“We have to wait to see what CMS has in store for us,” Dr. Zwerling said.

Michele Hall, a 54-year-old former attorney in Bradenton, Fla. who was diagnosed with Alzheimer’s late last year, said she was eager to start treatment with Aduhelm once it was approved.

Ms. Hall said her doctor at the Mayo Clinic in Jacksonville, Fla., told her she may be a good candidate for the drug but that he isn’t yet prescribing it.

A Mayo Clinic spokeswoman said its doctors aren’t prescribing Aduhelm because it is still “under review with our formulary committee, and no decisions have been made.” The process is independent of Medicare’s coverage decision, she said.

Ms. Hall said she can’t read or spell easily, and now uses a calculator to do math she used to do in her head. But she can still hold down a conversation with friends and do basic tasks—abilities she wants to retain for as long as she can.

“I said to my doctor, ‘How long is it going to take?’ Because time is ticking,” said Ms. Hall. “I look normal to everybody, but it won’t be too long from now that I can’t drive anymore and do things on my own. That’s coming for me and I know it, and I’d like to have this drug before then.”

Write to Joseph Walker at joseph.walker@wsj.com