The diagnosis was made during an MRI by Dr. David Altchek in New York.
Gonzalez pitched in 18 games (17 innings) after being acquired from Pittsburgh in the off-season for first baseman Adam LaRoche.
He had a record of 2-0 and an ERA of 1.59, with eight walks and 13 strikeouts.
His acquisition was intended to provide depth to Atlanta's bullpen, and his fastball consistently reached near 90 mph.
"It's part of our business," said Braves General Manager John Schuerholz on the team's Web site. "We're sad to lose him at this moment, but he's a young guy and determined guy. We'll get him back as healthy as ever."
"It (stinks) hearing that about one of your superstars," said catcher Brian McCann. "But we've got to move on. We need somebody to step in, in his place."