Federer, the winner of a record 17 majors and a five-time champion in New York, shut down his season to rest a knee injury which was aggravated in a semi-final loss at Wimbledon.
“Roger today is having the same injury issues, so I wish him a fast recovery,” Nadal said after beating Denis Istomin to make the second round.
Nadal had come into the tournament under an injury cloud after a serious wrist problem had forced an early withdrawal from the French Open as well as an absence from Wimbledon.
“It is very tough to see the players outside of the tour. The fans miss the players, the tour needs the players,” added the Spaniard.
World number one Djokovic, who beat Federer to win a second US Open last year, also felt sympathy for the 35-year-old Swiss.
“It’s not the same when you don’t have Roger for the tournament, for the fans. He’s been one of the most popular players of all time, one of the most successful players of all time,” said the Serb, a first round winner over Jerzy Janowicz on Monday.
“There is no doubt that every tournament is missing him.
“But on the other hand, we have got to focus on the players that we have at the moment. So I think even without him, it’s a very strong field. I’m sure it’s going to be a good tournament.”