The defenseman is second on the Predators with 16 points (two goals, 14 assists) in 25 games this season, behind forward Filip Forsberg (27 points). Josi, the Nashville captain, had one assist in 25:08 of ice time and scored in the shootout Sunday when the Predators won 4-3 at the Dallas Stars.
"Roman is such a valuable guy on the ice as well as off the ice," Nashville coach John Hynes said. "What you do miss when your captain is out of the lineup is just the voice in between periods. No one is going to replace him on the ice or off the ice, but if guys step up just a little bit in their roles and experience, it always helps."
The Predators lost at the Carolina Hurricanes 4-3 in overtime on Tuesday.
"He's our leader back there and we're going to miss him," Nashville defenseman Matt Benning said. "Guys did a great job, guys worried about their own game. I thought our game was really good."
Last week, Nashville placed defenseman Ryan Ellis (upper body, out 4-6 weeks), forwards Matt Duchene (lower body, 3-5 weeks) and Luke Kunin (lower body, 2-4 weeks), and goalie Juuse Saros (upper body) on injured reserve.
The Predators (11-14-0) are sixth in the eight-team Discover Central Division, eight points out of fourth place, which is the final Stanley Cup Playoff spot.
Josi scored 65 points (16 goals, 49 assists) in 69 games for Nashville last season, when he won the Norris Trophy voted as the best defenseman in the NHL.
"It's tough, especially with a guy like [Roman]," Nashville forward Ryan Johansen said. "The whole power play changes, just matchups and all those things. You can't really replace a guy like [Roman], but our guys did everything they could to have an impact for our club."
NHL.com independent correspondent Kurt Dusterberg contributed to this report