The defenseman, who did not join the team on its trip for a 7-0 loss to the New York Rangers at Madison Square Garden on Sunday, was injured in the first period of a 3-2 overtime loss to the Winnipeg Jets on Saturday.
Josi leads the Predators with 59 points (18 goals, 41 assists) in 67 games this season.
"It's upper body and right now it's day to day because they're trying to figure out what," Nashville coach John Hynes said. "He got hit in a different situation, so before they diagnose what it is, whether it's neck or head or his shoulder, before they do that we're just trying to wait and see."
Jordan Gross replaced Josi in Nashville's lineup against New York after being recalled from Milwaukee of the American Hockey League prior to the game. Gross was minus-1 with one shot on goal in 19:21.
Along with Josi, the Predators also remained without defensemen Ryan McDonagh and Alexandre Carrier, each day to day with an upper-body injury, and forwards Ryan Johansen (surgery on right leg) and Filip Forsberg (upper body).
Hynes said "there's a possibility" McDonagh, who missed his fourth straight game, could play this week, but that Forsberg, who missed his 18th straight, is not close to returning.
Johansen is expected to miss the rest of the regular season, the Predators announced Feb. 24.
Nashville (34-26-8) is five points behind Winnipeg for the second wild card into the Stanley Cup Playoffs from the Western Conference. The Jets have played three more games.
"They've handled it really well," Hynes said. "Guys have come up and played well. It's a hungry group. There are certain challenges that we have, but they're really committed. I think guys have come up and played with some swagger offensively."
