His withdrawal came shortly before his scheduled second-round match against American upstart Donald Young.
"I am really, really disappointed because it’s an important tournament for me," the Frenchman said on the tournament’s Web site. "With my illness, I'm sure I can't win this match."
Tuesday, Gasquet beat Sergio Roitman, 7-5, 6-1, 6-2, in the first round, while Young beat Chris Guccione, 6-7 (2-7), 6-3, 6-2, 6-3, to get his first win in a Grand Slam tournament.
"I'd prefer to win it, but I’ll take this also," Young said.