He suffered the injury in Toronto's 7-4 win Thursday over the Colorado Avalanche, but team officials did not disclose how it happened before Saturday's contest against the Pittsburgh Penguins.
To date, Kaberle, 30, has 30 points (four goals, 26 assists) in 49 games, making him a prime commodity before the NHL's March 4 trade deadline.
The club recalled defenseman Anton Stralman from their American Hockey League affiliate, the Toronto Marlies, to fill their roster vacancy.
"He moves the puck better than most guys in the league," said Coach Ron Wilson. "So obviously we're going to miss him."