Bernard Madoff, who is serving a 150-year sentence in North Carolina for running a fraud scheme that cost investors billions of dollars, was physically assaulted by another inmate in December, according to three people familiar with the matter.

After the attack, Mr. Madoff, who pleaded guilty a year ago and was sent to a federal prison in Butner, N.C., was moved on Dec. 18 to the prison's low-security medical center for treatment. At the time, the Bureau of Prisons said that rumors of an assault were false and that Mr. Madoff...