An expected rainstorm and heavy winds later on Saturday caused them to take the pre-emptive decision.
The women's final had been scheduled to start at 7pm local time on Saturday at Flushing Meadows. The revised start time has not yet been decided.
Saturday afternoon saw torrential rain and even a tornado warning in the New York area which remains in effect 9pm local time (2am UK time).
The weather could further complicate matters at the roof-less Arthur Ashe Stadium.
Rain delayed the start of Saturday's men's semi-final between Olympic champion Andy Murray of Britain and Tomas Berdych of the Czech Republic for 90 minutes before they were able to take the court.
They are scheduled to be followed by the second semi-final, pitting defending champion Novak Djokovic of Serbia against Spain's David Ferrer, although more threatening weather is in the forecast.
The men's final is scheduled to be played on Sunday afternoon.
Further delays could extend the championships to a Monday finish, which would mark the fifth year in a row that the year's final Grand Slam could not be completed by Sunday as scheduled.