Emergency workers attempted to rescue the workers from the rubble, but they were both pronounced dead after being pulled from the trench.
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The airport said to expect traffic delays in the area due to the recovery efforts near Terminals 5 and 7.
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New York firefighters first received the call about the construction accident at 11:25 a.m.
Some 12 units with 60 firefighters responded to the scene, but the workers could not be saved.
The Port Authority of New York and New Jersey issued a statement saying that a stop order for all construction at JFK has been issued.
The Port Authority said it is conducting a thorough investigation and will cooperate with all other investigative agencies.