Tournament organisers refused to divulge the identity of the player but Paire, who was removed from the draw on Sunday, later confirmed on social media that he had tested positive.
French players Adrian Mannarino, Kristina Mladenovic and Edouard Roger-Vasselin were placed under an "enhanced protocol plan" for players who might have been potentially exposed to the virus, allowing them to continue competing in the tournament.
Last month Pella and Bolivia's Hugo Dellien were removed from the Western & Southern Open, played in New York before the U.S. Open, after their fitness trainer tested positive for COVID-19 while they were all within the tournament's controlled environment.
Pella said he and Dellien were "unfairly quarantined" for 14 days.
- Murray: 'It was pretty emotional hearing from friends and family'
- Serena progresses at US Open in pursuit of elusive 24th Grand Slam title
- Andy Murray: The man who refuses to lose
"... I'm happy for them (French players) to be playing right now, but I want to know why they (USTA) did that with us, didn't give us any information," Pella told reporters after his first-round defeat by Jeffrey Wolf on Tuesday.
"I'm mad at them because of that. Because they changed the rules when Benoit tested positive... I just want some answers, because everyone in my situation would like the same thing.
"I was in quarantine unfairly for 14 days... and I know for sure that when Paire got his positive test, right away he got a second one. My trainer didn't... for four or five days because they said the New York health department does not do another test if you test positive."
A spokesperson for the USTA told Reuters on Monday that the organisers built the "enhanced protocol plan" in consultation with the New York City Department of Health and Mental Hygiene.
Several players have spoken out against the treatment of Pella and Dellien and Canadian Vasek Pospisil said on Tuesday that it was one of the triggers to launch the PTPA, a new players body, hastily before the U.S. Open.
US Open: Serena Williams favourite to win record-equalling Slam