The Food and Drug Administration’s acting commissioner, Janet Woodcock, is taking the highly unusual step of asking for a federal investigation of doctors within her own agency who met with the makers of an Alzheimer’s drug before the medicine’s recent approval.

Dr. Woodcock, in a letter made public Friday, called for the Office of Inspector General of the Department of Health and Human Services, which oversees the FDA, to review interactions between the drugmaker and FDA staff during the approval process.

The drug’s approval has been highly controversial, partly because of its annual price pegged at $56,000, and partly because evidence of the drug’s effectiveness was inconclusive.

During the time when the agency was considering the drug, called Aduhelm, FDA reviewers met with the company, Biogen Inc., that makes the drug. They collaborated with the company to prepare a joint review document presented to an FDA panel of outside advisers at a public meeting in 2020. The watchdog group Public Citizen called in December for an inspector general investigation “to scrutinize the unprecedented close collaboration.”

Michael A. Carome, director of Public Citizen’s Health Research Group, said the “investigation must be broad and assess when Dr. Woodcock first became aware of this collaboration and whether she ever specifically endorsed or facilitated it in any way,” and examine the FDA culture which allowed collaboration between the agency and the industry it regulates.

Dr. Woodcock didn’t respond to a request for comment.

In an email, a Biogen spokesman said the company “will, of course, cooperate with any inquiry in connection with a possible review of the regulatory process.”

The FDA initially approved the medicine for use in all of the approximately six million Americans who suffer from Alzheimer’s. On Thursday, the agency curtailed the recommended use, limiting it to patients with early-stage symptoms of Alzheimer’s.

That step brought the FDA recommended usage of the drug in line with the patients who were studied in the clinical trials Biogen used to seek approval of the drug, known generically as aducanumab. Biogen has said it would market the drug for use in early-stage patients with deposits of a sticky substance known as amyloid linked to Alzheimer’s.

Analysts project the drug could eventually ring up billions of dollars in yearly sales, largely paid by Medicare, which insures most Alzheimer’s patients in the U.S.

Dr. Woodcock’s letter was addressed to Christi Grimm, principal deputy inspector general of HHS, who is President Biden’s nominee to become inspector general.

Dr. Woodcock wrote that while she has “tremendous confidence in the integrity of the staff and leadership” of the FDA team that reviewed the drug, she is calling for an independent review of their actions.

“There continue to be concerns raised, however, regarding contacts between representatives from Biogen and FDA during the review process, including some that may have occurred outside of the formal correspondence process,” she wrote. “To the extent these concerns could undermine the public’s confidence in FDA’s decision, I believe that it is critical that the events at issue be reviewed by an independent body such as the Office of the Inspector General in order to determine whether any interactions that occurred between Biogen and the FDA review staff were inconsistent with FDA policies and procedures.”

“It would be extremely helpful,” she wrote, “if you could undertake this review as soon as possible.”

—Joseph Walker contributed to this article.

Write to Thomas M. Burton at tom.burton@wsj.com