No injuries were reported from the manhole fires at around 8 p.m. at West 50th Street near Eighth Avenue.
But a representative for the theater complex New World Stages said patrons were evacuated as a precaution.
"Thankfully, no one was hurt," said Michael Coco, senior director of theater operations for the Shubert Organization.
The plays that were canceled for the night also included "The Play That Goes Wrong," ''Puffs" and "As Spirited History of Drinking."
Photos posted on social media show flames shooting into the air. Tim Teeman, a senior editor at the Daily Beast, posted on Twitter that he was inside the theater complex when he heard "4 or 5 bangs/explosions" and smelled smoke.
The Fire Department says the fires were under control by 9:15 p.m.
Subway trains skipped the 50th Street station on the C and E lines while firefighters investigated.
A spokesman for Consolidated Edison said no one lost power. The cause of the fires was not known.