Center fielder B.J. Upton replaced Simmons in the leadoff spot Saturday night for Atlanta. Ramiro Pena was set to start at shortstop and bat eighth.
Simmons was injured while sliding headfirst into second on a stolen base in the third inning of Friday night's 4-1 win over Chicago. He stayed in the game and finished 0 for 4 with a run scored and a walk.
Simmons said his thumb swelled up overnight. He hopes to return to the lineup Sunday, adding that he feels fine.
A broken right pinkie landed Simmons on the disabled list for two months last year. He was hurt sliding headfirst into second on July 8 at Philadelphia.