Karl hurt himself during a preview performance Friday, forcing the cancellation of Saturday's matinee. Understudy Andrew Call was to fill in for him at the Friday night performance.
In a statement Saturday, producers said the musical is scheduled to open Monday at the August Wilson Theatre, with further performance information to follow. They declined to address the question of whether Karl would appear.
On Instagram, Karl posted that he tweaked his knee after a "poorly landed leap frog" and intended to see a medical specialist before going back on stage. He finished Friday's performance despite the injury, with help from a cane and his fellow actors, and was checked by a doctor.
"Groundhog Day" is based on the much-loved 1993 movie about a jaded weatherman forced to live the same day over, with Karl starring in the Bill Murray role of Phil Connors, a part Karl originated in London to critical acclaim.
The musical's script is by Danny Rubin, who co-wrote the film and keeps it faithful to the spirit of the original. Composer-lyricist Tim Minchin and director Matthew Warchus are the team behind "Matilda: The Musical," the Roald Dahl-inspired show that won seven Olivier Awards and four Tonys.
Karl received Tony nominations for his work in two other Broadway musicals, in "On the Twentieth Century" in 2015 and "Rocky" in 2014.