Kucherov, the NHL's leading scorer with 82 points (33 goals, 49 assists) in 63 games, missed Tampa Bay's 2-1 loss against the Buffalo Sabres on Wednesday and took part in the morning skate Thursday.
The Lightning, 4-0-1 in their past 5 games and 12-5-1 in their past 18, have the best record in the NHL and hold a five-point lead on the Toronto Maple Leafs for first place in the Atlantic Division.
The Stars, 3-4-0 in their past seven games following a five-game winning streak, hold the first wild card into the Stanley Cup playoffs from the Western Conference, with a two-point lead on the Anaheim Ducks and St. Louis Blues. Dallas trails the Minnesota Wild by three points for third place in the Central Division.