His injuries occurred in Friday night's 3-1 loss to the Chicago Blackhawks.
He was involved in a knee-on-knee collision collision with Blackhawks defenseman Jim Vandermeer.
Vandermeer was assessed a major penalty for kneeing and a game misconduct.
Maple Leafs General Manager John Ferguson Jr. said the 32-year-old Peca underwent successful surgery Saturday and is expected to miss up to four months.
"We look forward to having Michael back in the playoffs," Ferguson told the Toronto Sun. "Michael is a difficult commodity to replace, given the leadership he's brought to this team."
Peca, who signed with the Maple Leafs signed as a free agent before the start of the season, has played in 35 games this season and has four goals and 11 assists.
In 728 games, he has 164 goals and 245 assists.