Sources told the New York Post the "Entourage" star and reputed party animal has complained of exhaustion in recent weeks. He has been starring in the show since October and was scheduled to continue doing eight performances a week until Feb. 22.
The newspaper reported that Piven called in sick for Tuesday's evening performance and Wednesday's matinee and night-time shows, then flew home to Los Angeles Wednesday night.
An estimated $20,000 in refunds has already been given out due to the fact Piven missed performances this week, the Post said.
Daily Variety quoted Piven as saying he is suffering from a sickness related to his "high level of mercury."
The entertainment industry trade newspaper said the complaint prompted playwright Mamet to quip, "My understanding is that he is leaving show business to pursue a career as a thermometer."
The Post said representatives for the 43-year-old actor did not offer details about his health.