Dickey said he felt the spasm while running to first base in the fourth inning. He pitched the fourth and fifth innings from the stretch, then left the game after throwing just 67 pitches.
Eric O'Flaherty replaced Dickey on the mound to start the sixth inning. Dickey, in his first season with the Braves, has a 3.80 ERA through four starts.
His next scheduled start would be next week at SunTrust Park, also against the Mets.
Danny Knobler is a contributor to MLB.com based in New York and covered the Braves on Thursday. This story was not subject to the approval of Major League Baseball or its clubs.