Rodriguez went 0-for-4 with two strikeouts in the Yankees' 2-0 loss to the Blue Jays. In the second, he left two men on when he bounced out to second to end the inning, wasting one of the Yankees' few scoring opportunities.
On Sunday at Fenway Park, Rodriguez was pinch-hit for in the fifth inning because of tightness in his right calf. He previously had left hamstring issues. Heading into Tuesday night, Rodriguez had been the DH in the previous five games.
Joe Girardi has started A-Rod at DH the last six games -- and the manager indicated that he may have to put him there the rest of the season.
"At this point, I'm only just thinking about getting in the lineup," Rodriguez said.
After the Yankees' loss on Sunday, Rodriguez said he hurt the calf running out of the batter's box in the third inning. He felt it further, he said, when he ran the bases on Robinson Cano's subsequent double.
Rodriguez missed the first four months of the season as he rehabilitated his surgically repaired hip. He returned on Aug. 5 in Chicago against the White Sox. On the day he played his first game of 2013, he was suspended by baseball for violating MLB's Joint Drug Agreement and the Collective Bargaining Agreement.
On the season, Rodriguez, 38, is hitting .275 with six home runs and 14 RBIs in 37 games.
The Yankees lost their fourth straight game and trail Tampa and Texas by 3½ games.
"We have to get going," Rodriguez said. "We are running out of time."