The Predators, who have won four of five, made the moves Tuesday afternoon after the trio didn't take part in the morning skate before a game against Carolina.
During Tuesday night's game, goaltender Juuse Saros was injured in a collision with Carolina forward Nino Niederreiter.
At 5:15 of the first, Saros skated behind the Nashville net to play the puck. As Niederreiter skated through, they collided head-to-head. Niederreiter was assessed a minor penalty for roughing on the play.
Saros finished the first period, but was replaced by Pekka Rinne to start the second.
Ellis will be out up to six weeks with an upper-body injury. The defenceman hadn't missed any of Nashville's first 21 games and trails only Filip Forsberg and Roman Josi for scoring with nine points. Ellis played 26 minutes, 8 seconds in the Predators' 3-1 win over Columbus on Sunday.
Kunin is expected to miss two to four weeks with a lower-body injury. He has played 17 games and has two goals and three assists.
Johansen becomes the Predators' third player to land in the NHL's COVID-19 protocol, and first since Mikael Granlund spent the first eight days of the season on the list in quarantine after arriving from Finland before being cleared on Jan. 21. Lucas Sbisa also spent the first two days of the season in the protocol.
The centre has only been back four games after an upper-body injury Feb. 4 against Florida. Johansen has only five assists and has yet to score a goal this season.