Game 3 is Sunday in Columbus.
Kucherov, who led the league in scoring with 128 points (41 goals, 87 assists), is the favorite for the Hart Trophy, given to the league's MVP.
The Lightning matched the NHL's record for regular-season wins (62) but have been one of the biggest disappointments early in the playoffs, losing their first two games to the Blue Jackets, who snuck in with the Eastern Conference's final wild-card spot.
Kucherov had a phone hearing with the Department of Player Safety on Saturday morning and was not a part of the Lightning's line rushes during practice in preparation for a potential suspension.
Kucherov was given a five-minute major and a game misconduct for the hit on Nutivaara, which occurred at 15:34 of the third period. The DOPS determined that on the play, Kucherov skated toward the "defenseless Nutivaara, lowered himself for contact, and drives him into the boards," according to a video explanation released on Saturday.
The DOPS determined that the hit wasn't "excessively violent or forceful," but there were "several factors to elevate the play for supplemental discipline." Among them: Kucherov was in control of the play at all times. Kucherov was the one to initially trip Nutivaara to the ice, and while Nutivaara attempted to regain his footing, he remained in a defenseless position until Kucherov drove him into the boards.
"Kucherov takes advantage of this situation to deliver a dangerous hit to a player in an exposed and defenseless position," the video stated.
The DOPS determined this play fell into the category of "message sending."
The Blue Jackets were winning 5-1 at the time of the incident.
"While we understand frustration can occur at the end of the game, dangerous or retaliatory plays delivered in the final minutes of a playoff game will be viewed in context and punished accordingly," the video stated.
Kucherov has been fined once previously in his career.
The Lightning also will miss another star player for Game 3, as defenseman Victor Hedman did not participate in warm-ups after coach Jon Cooper called him a game-time decision to play.