The first Grand Slam since tennis resumed is due to begin on 31 August at Flushing Meadows in New York.
The Australian, 24, was also set to play in the Western and Southern Open.
"There are still significant risks involved due to Covid-19 and I don't feel comfortable putting my team and I in that position," Barty told the Australian Associated Press.
"I wish the USTA all the best for the tournaments and I look forward to being back in the US next year."
World number two Simona Halep and 2019 US Open champion Bianca Andreescu have not entered the lead-up tournament.
Barty said she will make a decision on whether to defend her title at the rescheduled French Open, which is due to begin on 27 September, "in the coming weeks".
Russell Fuller, BBC tennis correspondent
Assuming the US Open does go ahead - and the US Tennis Association still seems fiercely determined to stage it, despite numerous unanswered questions about quarantine - Barty will not be the only high-profile player absent.
If Halep and Andreescu do not play in the Western and Southern Open, which will take place at Flushing Meadows in the week before the US Open, then they seem very likely to skip the Grand Slam as well.
Many other players, though, are keeping their options open.
Both Novak Djokovic and Rafael Nadal appear in the entry list for the Western and Southern Open, although that does not mean they will definitely play.
The entry list for the US Open is due to close on Monday, by which time the USTA may well have confirmed its plans to stage this year's tournament behind closed doors.