They were protesting a new Russian law banning "propaganda on nontraditional sexual relationships," which was signed in June by President Vladimir Putin.
Before the start of the performance on September 23, one man in the audience shouted, "Putin, end your war on Russian gays!"
The protester also criticized the performance's two Russian stars, opera singer Anna Netrebko and conductor Valery Gergiev.
Both Netrebko and Gergiev were vocal supporters of Putin in his last election.
The man addressed the two, shouting, "Anna, your silence is killing Russian gays!
Valery, your silence is killing Russian gays!"
Gay-rights activists also staged a protest outside the Metropolitan Opera before the performance began.