McFarland last pitched on Saturday against the Braves, then he reported the discomfort Sunday.
"He's been throwing and it's been improving, and he's been feeling better and better," Lovullo said. "Yesterday we just felt like it made too much sense to send him out to get examined, just to make sure everything was OK."
Lovullo said the team expects McFarland to fly to Houston on Thursday night, where the D-backs open a three-game series with the Astros on Friday.
McFarland's absence leaves the D-backs with two left-handers in the bullpen -- Jake Diekman and Andrew Chafin.
Having three lefties in the bullpen is not as crucial during the Astros series, as Houston is a right-handed-heavy team. But starting Monday, the D-backs play nine games against the Cubs, Rockies and Dodgers -- all of whom have left-handed hitters that Arizona would like to be able match up against.
McFarland has been a valuable weapon for the D-backs this year, filling at times the role of long reliever and at other times being called on with runners on base to get a double play. He is 2-2 with a 2.00 ERA in 47 games.