Zibanejad, the Rangers leading scorer with 11 points (four goals, seven assists), is day to day with an upper-body injury. Filip Chytil will take his place in the lineup after being recalled from Hartford of the American Hockey League on Monday.
The Lightning could be without centers Brayden Point and Anthony Cirelli; neither took part in the morning skate and coach Jon Cooper said each is questionable, although not likely to play.
The Lightning, who were defeated 3-2 in overtime by the Nashville Predators on Saturday, are playing the first of five in a row away from home on a 12-day road trip that features two games in Stockholm against the Buffalo Sabres as part of the 2019 NHL Global Series.
The Rangers are coming off a 7-4 loss against the Boston Bruins on Sunday and have lost six of their past seven games (1-5-1).