Murray has been struggling with injury and has not featured since his Wimbledon quarter-final loss to Sam Querrey in July.
Murray, seeded number two, was training in the build-up to the final Grand Slam of the year and only revealed his decision after the draw was made.
His withdrawal caused Nadal and Roger Federer to both be in the same half of the draw, preventing a potential meeting between the two in the final in New York.
"I always thought that he was going to play if he was here practising," Nadal said, as quoted on Metro. "It was a little bit strange that he retired just the morning after the draw was made."
"It is something that is a little bit strange and difficult to understand, but the worst thing is he is not healthy and I wish him a very fast recovery. Injuries are bad for everybody. I know better than all of them, so I wish him a fast and good recovery. That's the most important thing.
"Normally you want to keep practising, keep trying until the last moment. You retire on Monday morning or Sunday afternoon, not Saturday morning. If not, you can do it before the draw.
"That's why I say it is strange. But of course he has his reason, and for sure the negative news was that he will not be playing here."
Had Murray withdrew earlier, Nadal and Federer would have been on opposite sides of the draw.
And with the duo being the main favourites in Flushing Meadows, it would have set up a potential first-ever meeting in the US Open between the long-time rivals in the final with the world number one ranking up for grabs.
Meanwhile, Nadal and Federer both advanced to the second round of the US Open after their wins on Tuesday (29 August).