Ortiz pinch-hit in the eighth inning of the Red Sox's 4-3 walk-off victory, but Braves manager Fredi Gonzalez elected to intentionally walk the slugger, who was then lifted for a pinch-runner.
Ortiz had the same injury at the end of Spring Training and sat out the final five games of the Grapefruit League schedule.
Ortiz's workload over the past few games has been more than normal. He started both games at first base against the Braves and legged out a single in Wednesday's game against Atlanta.
"You're dealing with a lower extremity. I just think coming off the volume, David's been great in terms of the preventative maintenance and the care that he's got to go through," Farrell said. "And yet, after two full days at first base and another at DH last night, it was best to hold him out tonight."
A.J. Pierzynski, who originally had the night off, went 2-for-4 serving as Boston's DH.
Farrell expects Ortiz to start Friday's game against the Rays.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. Quinn Roberts is a reporter for MLB.com This story was not subject to the approval of Major League Baseball or its clubs.