Smith was in the original starting lineup Tuesday for the second game of a four-game series against the Phillies, but complained of soreness after hitting in the indoor cage and then jogging in the afternoon.
Black said there was a chance that Smith would be available to pinch-hit Tuesday but that he wouldn't start on Wednesday against left-handed pitcher Cole Hamels. Smith, who is a left-handed batter, is hitting .266 this season with 12 home runs and 44 RBIs.
He's hitting .132 this month with five hits in 42 plate appearances.
Rymer Liriano got the start in right field in Smith's place.