Federer, who at seventh is seeded in his lowest position at the US Open since 2002, suffered his earliest Grand Slam exit since winning his first Grand Slam title a decade ago with a second-round loss at Wimbledon this year.
The Basel native, with a men's record 17 Grand Slam crowns but no US Open title since his fifth in a row in 2008, opens in a night match in New York against Slovenia's Grega Zemlja, who has not taken a set off Federer in two prior meetings, most recently at Rotterdam in February.
Federer will match a record by making his 56th consecutive Grand Slam appearance, a remarkable run that began at the 2000 Australian Open.
Wayne Ferreira set the mark with a run that ended at the 2004 US Open.
"I've put in the hard work for so many years,” Federer said.
“That keeps my base at a very high level," he said.
"It's actually more comfortable with my body today than it has been in the past."
Meanwhile, second seed Rafael Nadal, also a reigning French Open champion, launches his quest for a 13th career Grand Slam title against US wildcard Ryan Harrison.
The Spaniard defeated Harrison in their only prior meeting, which came in Nadal's first hardcourt match of the year in March at Indian Wells after a seven-month knee injury layoff.
Nadal went on to win at Indian Wells as well as this month at Montreal and Cincinnati and enters this US Open with a 15-0 hardcourt record this season.
"It has been great," Nadal said.
"But there's no time to think about what happened," he said.
"It's only time to think about what's going on," Nadal said.
"What's important is (to) try to be ready for the first round of the US Open.
"I have a tough opponent in front of me, Ryan Harrison, and I am focused on that. I hope to be ready to play well. I hope to be very competitive for the first match."
Nadal, who would take home $3.6 million (2.69 million dollars) by winning the title, would also end Novak Djokovic's reign as world number one, if the Serb star also fails to reach the final for a fourth year in a row.
In women’s action, top-seeded Serena Williams starts defending her US Open crown on Monday against Italy's 54th-ranked Francesca Schiavone in the opening night match on the Flushing Meadows hardcourts.
Williams is seeking her 17th Grand Slam singles crown and her fifth US Open title.
"It will be a good match," Williams said.
"She's a really good player," she said.
"She's a big fighter and she's dangerous."
Her older sister Venus Williams, a seven-time Grand Slam champion who has been nagged by back pain and last reached a Slam semi-final at the 2010 US Open, has a tough first-round match with Belgian 12th seed Kirsten Flipkens.
Flipkens beat her 0-6, 6-4, 6-2 at Toronto earlier this month.
US 15th seed Sloane Stephens, a possible fourth-round foe for Serena Williams, opens against Luxembourg's Mandy Minella.
Stephens ousted Serena Williams in the Australian Open quarter-finals and reached the last eight at Wimbledon as well.
UPDATE: Federer's opening match was postponed until Tuesday because of rain.