Madoff was convicted of running a Ponzi scheme that lost investors billions of dollars. He pleaded guilty to 11 felony counts and was given a 150-year prison sentence.
Neither prison authorities, nor Madoff's attorney, Ira Sorkin, would verify the account, but sources said Madoff suffered a broken nose, fractured ribs and various lacerations in an altercation over a money matter, the Journal said.
Madoff allegedly owed another inmate money, the report said.
A Bureau of Prisons spokeswoman, Traci Billingsley, said, "not one inmate told staff he was assaulted."
Billingsley also said the inmate allegedly involved in the incident lived in a different area that was locked down at night and that it was "virtually impossible," for the assault, as described, to have occurred.
One former inmate said Madoff had given him some financial advice, specifically telling him to avoid day trading. "I was trying to get into day trading and he's like, 'That's not for you. That's for individuals like me with millions to spare,' " the former inmate said.
Copyright 2010 United Press International.