No other details, including when the injury occurred, were immediately known. Josi skated more than 25 minutes in a win over the Dallas Stars on Sunday and scored the shootout winner.
The reigning Norris Trophy winner has seen his numbers dip this season as the Predators sit outside of a playoff spot in the Central Division. The 30-year-old has two goals and 16 points with a minus-12 rating through 25 games.
Josi will join injured stars Matt Duchene, Ryan Ellis and Juuse Saros on the injured reserve.
The Predators return to the ice Tuesday against the Carolina Hurricanes. Ahead of that game, forwards Mathieu Olivier and Rem Pitlick, as well as defenceman Jeremy Davies, were recalled from the taxi squad.