Coach Dan Bylsma says Kobasew was hurt in the first period of Monday's 3-1 win over the Carolina Hurricanes. Kobasew, who signed with Pittsburgh as a free agent in the off-season, has two goals in 12 games for the Penguins.
Kobasew's injury came one game after the Penguins lost defenceman Rob Scuderi with an ankle injury that will require surgery.
The Penguins are already playing without forward James Neal (upper body), forward Beau Bennett (undisclosed injury) and goaltender Tomas Vokoun. Vokoun is out until at least January while he recovers from a blood clot.
Pittsburgh forward Brandon Sutter did not practice on Tuesday. His status for Wednesday's game against Boston is unclear.