The show had no scheduled performances on Sunday, and a spokesman said a decision would be made later in the weekend about whether the opening, scheduled for Monday night, would proceed.

“Groundhog Day” has been one of the most anticipated new musicals of the current Broadway season, after a well-received production at the Old Vic Theater in London. At the Olivier Awards — London’s analog to the Tonys — on April 9, “Groundhog Day” was named the best new musical, and Mr. Karl, who led the British production, was named the best actor in a musical.

The show, produced by Whistle Pig, Columbia Live Stage, and The Dodgers, is also among the more costly of the season. It has been capitalized at up to $17.5 million, according to a filing with the Securities and Exchange Commission.

The musical, featuring a score by Tim Minchin and a book by Danny Rubin, is adapted from the 1993 film, starring Bill Murray, about a man doomed to relive the same day again and again.

Mr. Karl is a highly regarded Broadway actor, and “Groundhog Day,” which was developed around his performance, is expected to be a breakout role for him. His last two Broadway-musical appearances, as a self-regarding film star in “On the Twentieth Century” in 2015 and in the physically strenuous title role of “Rocky” in 2014, were both nominated for Tony awards, but “Rocky” was a disappointment because the show flopped.