Manager John Gibbons said Donaldson, the reigning American League MVP, aggravated a lingering injury and is listed as day-to-day.
"The calf just sort of locked up," Donaldson said. "I tried to go three or four innings with it. It was just one of those situations where one, I didn't think I was quite able to play defense the way I wanted to, and two, if I had to try and run, it was pretty difficult. But I don't think it's too serious and, hopefully, I'll be back for our next game."
Donaldson, who hit a three-run homer in the third off Matt Moore, exited in the seventh inning after he was unable to run out a ground ball in the 5-3 loss. He limped back to the dugout and was replaced at third base in the bottom of the inning by Darwin Barney, who moved over from second base.
Ryan Goins took over for Barney at second.
The Associated Press contributed to this report.