Federer, ranked third in the world, is searching for his third Grand Slam title of the year, following his success at the Australian Open in January and Wimbledon in July.
His biggest title rival is Spain’s Nadal, who beat Serbia’s Dusan Lajovic in his opening match of the tournament.
In the women’s draw, French Open champion Jelena Ostapenko, seeded 12th, opens play on Louis Armstrong against Sorana Cirstea, while American 20th seed Coco Vandeweghe begins the night session against Tunisia’s Ons Jabeur.
Cincinnati Open champion Grigor Dimitrov, seeded seventh, is second on Louis Armstrong against Aljaz Bedene’s conqueror Andrey Rublev before sixth seed Dominic Thiem plays 19-year-old American Taylor Fritz.
Argentina’s 24th seed Juan Martin del Potro is second on Grandstand against Spanish world number 148 Adrian Menendez-Maceiras.
Meanwhile, Jamie Murray, Dominic Inglot and Naomi Broady are among the Britons in action as the doubles competitions begin.
“My forehand’s painful, it’s just so annoying,” he told the trainer.
When fully fit, Kyrgios has shown the kind of form this year that has made him tipped as a possible Grand Slam champion, taking a rampant Federer to a final set tie-break in Miami and reaching his first Masters final in Cincinnati this month.
“I don’t know what to do, I really don’t,” he added on court.
“I’m feeling good, I finally had a good week last week, playing a good match, middle of the third set against an Aussie, and bang – that’s it.”
Millman goes on to face Tunisia’s Malek Jaziri or Thiago Monteiro of Brazil in the second round.
“I know Nick’s shoulder deteriorated as the match went on, so it’s a victory, but slightly hollow,” said Millan. “I feel for him.”