The 31-year-old has played sporadically over the last two seasons and contested only eight matches on the ATP World Tour this year.
The last of those was on Tuesday when he quit midway through the third set against Jarkko Nieminen at the US Open warm-up tournament in Winston-Salem, North Carolina, because of heat stroke.
"Friends, unfortunately my health won't allow me to compete this year at the US Open. Thank you for all your support," Fish tweeted on Wednesday.
Last year Fish, who suffers from an accelerated heartbeat, reached the US Open fourth round but handed Roger Federer a walkover after saying he had to withdraw for "precautionary measures" on doctor's orders. He was sidelined for the next six months before returning in Indian Wells in March.
However, his health has prevented him from competing in any best-of-five-set matches this year as he has not played at any of the four majors or the Davis Cup.