Farnsworth's last offering was a called third strike past the White Sox's Orlando Cabrera, ending the frame in Chicago's 7-6 victory over New York.
Yankees manager Joe Girardi said he had planned to send the right-hander out for the eighth inning before learning of the injury, which Farnsworth speculated could be an elbow strain.
"He slipped, and his arm felt a little funny," Girardi said. "We'll have to see how he is [on Friday]."
A soft landing area on the mound at U.S. Cellular Field was an issue for other pitchers as well. White Sox starter Gavin Floyd called out the grounds crew for work earlier in the game, and Yankees right-hander Joba Chamberlain also caught a spike in the ground.
Farnsworth said he has suffered similar injuries in the past but was not concerned that he would miss a significant amount of time. He expected to be examined when the Yankees arrive at Progressive Field in Cleveland on Friday.
"You definitely don't want to mess with anything there," Farnsworth said. "It's better to be safe than sorry."
The Yankees' bullpen will be in need of reinforcements without Farnsworth, as well as right-hander Brian Bruney, who has a strained right mid-foot and was in a walking boot before Friday's game.
A 51-minute rain delay also led the Yankees to turn to right-hander Ross Ohlendorf for two innings and 49 pitches in the loss, using him in relief of starter Phil Hughes for the top of the third inning.
"We'll probably have to make some moves," Girardi said.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.