The match on Arthur Ashe Stadium was halted in game two of the second set after a group of three protesters wearing t-shirts with the slogan “end fossil fuels” began chanting the same message.
Gauff and Muchova initially stayed on the court for about 10 minutes while security tried to deal with the situation.
The crowd at one point chanted “kick them out” with the protesters apparently being difficult to shift.
One of the protesters glued his feet to the stadium floor, causing the lengthy delay.
Gauff and Muchova both eventually left the court to return to the locker rooms.
Television footage showed the players trying to stay loose in the locker rooms, consulting with coaching staff.
The incident is the latest in a series of protests by climate activists targeting major sporting events around the world.
In July, three people were arrested after disrupting play at Wimbledon, scattering orange confetti and jigsaw pieces over the court.
In a separate incident at the Ashes cricket Test between Australia and England at Lord's in London in June, two men from the “Just Stop Oil” movement ran on to the field and scattered orange powder.
There were similar demonstrations during the recent World Snooker Championship and English Premiership rugby final.
The group has also targeted Premier League matches and the Formula One British Grand Prix at Silverstone.
Agencies contributed to this report