The vote would give authority to the strike "should management's intransigence warrant such an action," the union said in a statement to the Times.
The orchestra's contract, along with those of 15 other unions representing workers, expires July 31. The Times reports that the company's management is attempting to reduce labor costs at a time when ticket sales have decreased and its endowment has diminished.
The musicians in the Metropolitan Opera orchestra wore buttons during performances May 10-11 to draw attention to the fact that the opera house is seeking concessions from them in the contract talks.
"We remain hopeful that the negotiations will have a positive outcome," Jessica Phillips Rieske, a clarinetist who is the chairwoman of the orchestra's negotiating committee, said to the Times in a statement. "To maintain this level of quality, the Metropolitan Opera must compensate its musicians at a standard that allows this ensemble to continue to attract and retain world-class talent."