Left fielder A.J. Pollock replaced Rodriguez in the leadoff spot of the batting order while Jarred Kelenic slid over to centre in the field.
Rodriguez entered the game hitting a .236/.300/.445 slash line this season, with five home runs and 13 RBIs.
He was 1-for-3 at the plate Saturday, hitting a single to start the third inning and then stealing second base, but he was left stranded as Blue Jays starting pitcher Kevin Gausman struck out the side.
The 22-year-old earned the American League Rookie of the Year award plus a Silver Slugger Award while also competing in the All-Star Game.