WASHINGTON—At least two of the memos that former FBI Director James Comey gave to a friend outside of the government contained information that officials now consider classified, according to people familiar with the matter, prompting a review by the Justice Department’s internal watchdog.

Of those two memos, Mr. Comey himself redacted elements of one that he knew to be classified to protect secrets before he handed the documents over to his friend. He determined at the time that another memo contained no classified information, but after he left the Federal Bureau of Investigation, bureau officials upgraded it to “confidential,” the lowest level of classification.

The Justice Department inspector general is now conducting an investigation into classification issues related to the Comey memos, according to a person familiar with the matter. Mr. Comey has said he considered the memos personal rather than government documents. He has told Congress that he wrote them and authorized their release to the media “as a private citizen.”

Mr. Comey gave four total memos to his friend Daniel Richman, a former federal prosecutor who is now a professor at Columbia Law School, people familiar with the matter said. Three were considered unclassified at the time and the one was that was classified contained the redactions made by Mr. Comey.

As FBI director, Mr. Comey had the legal authority to determine what bureau information was classified and what wasn’t. Once he left government, however, the determination fell to other officials. The FBI deemed the memos classified sometime during 2017, one of the people familiar with the matter said.