Mladenovic, who is scheduled to play in a second-round doubles match on Saturday, voiced her displeasure with the conditions.
The match started after 5 p.m., with Mannarino going on to lose to Zverev in four sets.
Aussie Jordan Thompson won through to the fourth round with a straight-sets win over Mikhail Kukushkin, while seventh seed David Goffin brushed aside Serbia's 26th seed Filip Krajinovic 6-1 7-6 (7-5) 6-4.
The Frenchman is one of the 11 players facing extra restrictions because of his contact with Benoit Paire, who tested positive for Covid-19 on the eve of the tournament, and officials said he should have been in his room quarantining instead of playing Zverev.
Mannarino was one of several players put under enhanced safety protocols earlier this week after his countryman tested positive.
"Unfortunately I lost the match".
"They told me they were trying to contact some guys and see if this decision could be changed".
It was, but not before the government had a large effect on the outcome.More news: Daniel Prude: NY Attorney General to set up grand jury
"Andy Murray is a very special player", Eurosport tennis expert Alex Correja said.
"I'm not gonna call it a nightmare-that's for sure", Mannarino said.
Players and their immediate circle (coaches, physio, guests) are in Tier I. Media, tournament staff, officials and ballpersons comprise Tier II. "They put me in a situation I couldn't give my best on the court, so I'm not going to complain about that".
"The Zverev-Mannarino match was delayed while a collaborative dialogue with health officials was conducted today", the body said. "Communication with the players was ongoing during the afternoon to keep them updated at all times. Given the sensitivity of the medical issues involved, the USTA is not able to provide further details", the body added.
Mannarino, the lefty 32nd seed, had already been fined $2,500 when someone in his entourage failed to follow mask protocols.
In a post to her Instagram story on Friday morning, Flipkens wrote she and the other restricted players were now strictly quarantined to their rooms.
Mannarino said he has not considered hiring a lawyer over the matter.
World number one Novak Djokovic, who last week launched a breakaway players' body, said the communication process was not ideal but appreciated that health decisions were not always up to the organisers in NY.More news: US military sticks with Microsoft for US$10 billion Jedi cloud contract
Mannarino has been spotted on the grounds walking while being surrounded by security.
Shapovalov also looked set for an exit against American 19th seed Taylor Fritz. He drank from a water bottle and checked his phone while he was supposed to be on court at Armstrong.
The City actually allowed me to play with a new protocol on Sunday.
"I just felt like I had so many points that I didn't capitalise on".
Mannarino told reporters that he was thankful to those who helped him be able to play his match on Friday. "At the beginning I was a little bit cold".
"Benoit was positive, we don't even know if it was a false positive - there are quite a lot of false positive tests in sport I've been hearing". Kirsten Flipkens complained that she isn't allowed to leave NY and go home despite being eliminated from the tournament.
The state's hard line means the Open is in danger of more cancellations if another player tests positive across the final week.
One of them, Kristina Mladenovic, said after losing her second-round match: "It's like we are prisoners, or criminals. Hopefully I'll be able to continue the good performance that I had tonight". Give the opportunity to give him the chance.More news: Michael Cohen’s Memoir Features Disturbing Stories About Life With Trump
A group of seven players were found to have had close contact with Paire, but unlike Dellien and Pella, were not automatically removed from the US Open draw. I might be infected, I don't know.