The Braves made the announcement Thursday before their game against the St. Louis Cardinals.
Beachy (2-1, 4.50) allowed three earned runs and five hits in six innings of the 5-3 loss to the Mets. He was making his fifth start since returning from Tommy John surgery.
"He said he didn't like the way the last few innings went," Atlanta manager Fredi Gonzalez said.
Beachy, who underwent surgery on June 21, 2012, will be examined by Dr. James Andrews on Monday.
Mike Minor (12-5, 3.06) will start on Sunday in the finale of the four-game series at St. Louis.