Rajaratnam, founder of the Galleon Group, is serving an 11-year sentence for insider trading at a minimum-security Devens Federal Medical Center in Ayer, Massachusetts.
Malaszuk was Rajaratnam's driver for 15 years and the caretaker of his Greenwich estate, according to the lawsuit.
He alleges that during visits to his boss in prison, the onetime billionaire gave him names and contact information for the family members of about 20 other inmates at the facility who were to receive money.
"Mr. Rajaratnam secretly passed these pieces of paper to Mr. Malaszuk and ordered Mr. Malaszuk to make these wire transfers to fellow inmates in order to control these other inmates and have them do his bidding," according to the lawsuit.
The lawsuit cites a 2013 New York Post article, which reported that Rajaratnam had a personal servant at the prison, use of a private bathroom, and an adjustable bed.
The prison's public information officer did not immediately return a message Wednesday seeking comment.
Malaszuk alleges he lost his job after complaining to Rajaratnam that he didn't want to jeopardize his own freedom by conducting illegal transactions for him.
Terence Lynam, Rajaratnam's attorney, said in a statement Wednesday that the allegations are false and "simply the latest in a long-running effort by an embittered former employee to extort money from Mr. Rajaratnam and his family."
Rajaratnam is scheduled to be released from prison in 2021. In his criminal case, he was fined $10 million and was ordered to forfeit $53.8 million. He also was ordered to pay a record $92.8 million civil penalty to the SEC.
His conviction was among more than two dozen in a case the government touted at the time as the biggest insider trading prosecution in history.