Play was scheduled to begin at 7pm ET (2300 GMT) on Thursday with world number one Serena Williams taking on Italian Roberta Vinci.
The delay puts the American's calendar-year grand slam bid on hold.
That match would have been followed by second seed Simona Halep against Flavia Pennetta of Italy.
An action-packed Friday marathon of action will now start at 11am ET with the Halep-Pennetta match, followed by Williams versus Vinci.