Tempers flared in the second period when Columbus captain Nick Foligno knocked Lightning goaltender Ben Bishop to the ice. A scrum ensued and Blue Jackets defenceman Dalton Prout came in heavy with a right hand to Kucherov, who was tied up with Foligno.
The NHL will review the play, and Prout could face further discipline.
Kucherov had to leave the game, which the Lightning won 4-0. The team had already lost forward Valtteri Filppula to an upper-body injury earlier in the game.
Lightning head coach Jon Cooper had no updates on his two injured players after the game, but said he doesn't think they'll miss too much time.
Prout received a two-minute minor for roughing and a 10-minute misconduct. Kucherov, the third man in the Foligno/Andrej Sustr scrum, was given two minutes for roughing.