The city virtually shut down at lunchtime in preparation for the arrival of the hurricane, which is expected Sunday morning and could cause widespread flooding and damage to buildings.
Rain disrupted practice for a number of players this morning and Flushing Meadows will shut at 1700 local time on Saturday (2200 BST) and will not open again until Monday morning, when the tournament is scheduled to start.
Federer said: "At my age you know what it takes to get ready, and you don't panic. I won't be playing tomorrow [Sunday]. It's not an issue. I'm not even going to try to. It wasn't on the plan anyway.
"But sure it's somewhat scary because we don't know how hard it's going to hit us. I've got family. We're in New York City and it's not just a regular city. It's quite something with all the buildings.
"So it's unusual, but we'll follow the news closely and we'll try to stay as safe as we can so we get through it."
Second seed Rafael Nadal is also expecting to have a quiet day on Sunday, and he added: "I'll just stay in the hotel, maybe watch some films.
"But we will see what's going on. I never had an experience with a hurricane. It's something new. I think it is very bad for the city, for the weekend, for everybody."
One man for whom it will not be a new experience is eighth seed and main American hope Mardy Fish, who spent his formative years in Florida.
He said: "It will be pretty surreal, I think. Obviously it doesn't happen a lot, but I've been through quite a few hurricanes living and growing up in Florida."
The closure of much of the city's transport links is proving a major headache for players who have been competing in tournaments outside New York and need to travel in ahead of the start of the tournament.
Among those affected are women's world number one Caroline Wozniacki, French Open champion Li Na, Wimbledon semi-finalist Sabine Lisicki and America's John Isner.
Lisicki said on Twitter: "All flights to NYC are cancelled for next few days...how are we going to get there!?!?"
Dutchman Robin Haase, a semi-finalist in Winston Salem this week and Andy Murray's possible second-round opponent at Flushing Meadows, added: "Car/train/subway/plain/boat. Nothing is possible at the moment to get to New York. Trying to teleport. Can't figure it out though."
When the tennis does start, Federer will be playing his first grand slam tournament as a 30-year-old after celebrating his birthday earlier this month.
The Swiss, a five-time champion at Flushing Meadows, played down the significance of the milestone but did look back to the 2005 final, when he beat 35-year-old Andre Agassi.
Federer said: "That was his 20th US Open in a row. I've got a way to go. This is my 12th time here in the main draw, so it's definitely an inspiration seeing guys being around for a long time like Ken Rosewall, Jimmy Connors, Andre Agassi.
"I feel my game allows me to still play for many more years because I have a relaxed playing style. I have almost played 1,000 matches on tour and that leaves its toll, but I'm very professional when it comes to massages, stretching, diet, sleep, all of that stuff.
"I have looked at the long term for a long time. I haven't been chasing (titles) around since I turned world number one seven years ago. That's why I'm confident I can still play for many more years to come at the highest of levels.
"(Turning 30) hasn't changed anything. I'm still as professional. I'm still as hungry. Everything's still completely normal. It's just a number that's changed. I'm ready to go."
Federer has not had the best preparation, losing in the third round in Montreal and the quarter-finals in Cincinnati, but he is happy with his form heading into the tournament.
"I feel good," he added. "I have had plenty of practice. There are no niggling injuries and everything is under control. It's always a great event to be a part of. I've had success here, obviously. It's nice to be back."