Karlsson, the reigning Norris Trophy winner for the NHL's top defenseman, sustained a laceration late in the second period when he was pinned against the boards by Pittsburgh's Matt Cooke.
The Senators said Swede Karlsson would require surgery and was out indefinitely.
"Obviously, the way he's playing and how much he means for us, for our team, it feels terrible," said Ottawa captain Daniel Alfredsson. "And I feel really bad for him."
Cooke said there had been no intent to injure Karlsson.
"It's a complete accident. Obviously, I feel terrible about it," Cooke said. "It's happened a few times over the past couple years, and it's scary."
Pascal Dupuis put the Penguins ahead in the first period before Ottawa grabbed a 2-1 lead through Stephane Da Costa and Jim O'Brien midway through the second.
James Neal restored the Penguins' lead with his ninth and 10th of the season before Sidney Crosby made the game safe with a wrist shot in the third.
Crosby also picked up a pair of assists for the Penguins (9-5-0), who welcomed defensemen Kris Letang and Matt Niskanen back to the team from injury. Ottawa (7-5-2) lost for the fifth time in seven games.
Senators goaltender Craig Anderson was coming off a 42-save shutout against the Sabres on Tuesday but finished with 26 stops against Pittsburgh. Karlsson had scored the opener in Ottawa's 2-0 win over Buffalo.
Marc-Andre Fleury had 27 saves for the Penguins, who moved within a point of Eastern Conference-leading New Jersey.
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