The match between seventh-seeded Federer and unseeded Grega Zemlja of Slovenia will be rescheduled for Tuesday, along with two other men's first-round matches that were halted in progress.
Vasek Pospisil of Canada was leading Brazil's Rogerio Dutra Silva 6-4 6-3 6-7 (9) 0-4 with the winner advancing to a second-round encounter with second-seeded Spaniard Rafa Nadal.
In the other suspended match, Colombia's Santiago Giraldo was leading Carlos Berlocq of Argentina 3-6 6-3 7-6 (6) 2-1. The winner of their contest will meet the winner of the Federer match in the second round.
Light rain began to fall just as top-seeded American Serena Williams completed her 6-0 6-1 thrashing for Italy's Francesca Schiavone on the centre court.
Forecasts were for continuing rain, which led to the decision to call an early end to the Opening Day schedule, officials said.
The US Open has been plagued by rain that has extended the schedule the last five years to a Monday finish.
The championships at Flushing Meadows this year had already been scheduled to end on a Monday.
Prior to Monday's opening match, US Tennis Association officials outlined recently announced plans to put retractable roofs on Arthur Ashe and Louis Armstrong stadium as part of a massive renovation expected to be finished by 2018 at a cost of $550 million.