The 22-year-old Karlsson's recovery will be at least three to four months, said general manager Bryan Murray in an update to reporters just before 1 p.m. ET at Scotiabank Place in Ottawa.
Karlsson, who won the Norris Trophy last year as the NHL's best defenceman, underwent surgery on the tendon Thursday morning at The Ottawa Hospital.
He suffered the injury when Pittsburgh Penguins forward Matt Cooke's skate blade came down on the back of the Swede's left leg as the two tangled along the boards. It happened in the second period of Wednesday night's game in Pittsburgh.
Karlsson fell to the ice and was in visible pain after tangling with Cooke. He needed help getting back to the bench and displayed frustration, throwing his stick against the boards before disappearing down the runway.
Sens not seeking suspension for Cooke
Cooke has been suspended several times for hits, some of them involving head-shots that injured opposing players.
In 2011, Cooke was suspended for the Penguins' final 10 regular-season games and the first round of the playoffs after an elbow to the head of New York Rangers' defenceman Ryan McDonagh.
The Senators responded in Wednesday's game in the third period when Chris Neil took penalties for roughing and a 10-minute misconduct after fighting with Cooke. Pittsburgh won the game 4-2.
Murray said Thursday the Senators have not pushed the league for a suspension.
The Sens GM also said he was not interested in a rebuild after the injury and said he would not "gut" the team, disputing any idea of trading the team's starting goalie, Craig Anderson.
The team is already missing centre Jason Spezza, out for the season after back surgery, and defenceman Jared Cowen, who is out for the season after hip surgery.