Cooper said the Lightning were hopeful that Kucherov would be able to play, but now they are unsure whether the reigning league MVP will return for Saturday's game against Anaheim.
Kucherov suffered the injury during Tuesday's loss to the St. Louis Blues and did not return to the contest.
The Lightning have not disclosed details about the injury, but Cooper told reporters after Tuesday's game that Kucherov was not in the concussion protocol.
Kucherov, 26, has six goals and 12 assists in 18 games this season. The three-time All-Star scored a league-leading 128 points last season, when he won the Hart Trophy, the Art Ross Trophy and the Ted Lindsay Award.