The 21-time grand slam champion, who has won three times at Flushing Meadows, was hoping the United States would change their long-standing rules to allow non-citizens without a coronavirus vaccine to enter the country.
The Wimbledon champion, who was also banned from playing in the Australian Open due to his anti-vaccination stance, said after his SW19 success in July that he was waiting "hopefully for some good news from USA".
That led to him remaining on the entry list for the tournament that begins on Monday despite not being in the country, but he has now withdrawn.
He said on Twitter: "Sadly, I will not be able to travel to NY this time for US Open. Thank you #NoleFam for your messages of love and support.
"Good luck to my fellow players! I'll keep in good shape and positive spirit and wait for an opportunity to compete again. See you soon tennis world!"
The Serbian's omission hands Nadal an advantage as he aims to add to his 22 grand slam titles, while world number one and defending champion Daniil Medvedev also has a smoother path.
The draw for the final grand slam of the year takes place later on Thursday in New York.