Sturridge and author Lyle Kessler's play were nominated for Tony Awards last week, however, the show will play its final performance May 19 after 27 previews and 37 regular performances at the Gerald Schoenfeld Theatre.
Slow ticket sales are to blame for the early closure, The New York Times said.
The Daniel Sullivan-directed production began performances March 26 and opened April 18. It was scheduled to run through June 30.
The show made headlines before it even opened when Foster replaced Shia LaBeouf, who left during rehearsals because of creative differences.