Kucherov left Game 5 on Saturday night with an apparent upper-body injury after he collided in the first period with Chicago Blackhawks goalie Corey Crawford and fell awkwardly into the post while trying to score. The Russian skated off slowly and didn't return in the Bolts' 2-1 loss.
Lightning coach Jon Cooper had said Kucherov, a key member of the team's "Triplets" line who is second in playoff scoring with 10 goals and 22 points, was "probable" for Game 6.
Bishop, who played in Game 5 after missing Game 4 with an undisclosed injury, got the start for Game 6 said Monday afternoon that he "is getting better every day."
The Blackhawks hold a 3-2 edge in the best-of-seven series and can clinch the Stanley Cup with a victory Monday night.
The Associated Press contributed to this report.