Thome, who leads the AL with 20 homers and 52 RBI, said he tweaked it in his last at-bat Thursday in Cleveland. Manager Ozzie Guillen's plan is to also keep his DH on the bench Sunday and with an off-day Monday hope that Thome will be ready to go Tuesday when Chicago opens a key series against first-place Detroit.
"It's definitely way better than it was yesterday," said Thome, adding the strain restricts his ability to push off when he hits.
"That's the frustrating thing. When you get those little injuries you want to be out there."
The White Sox had lost four straight before Saturday night's game and have not played well lately, even when Thome was healthy.
"To me, it's more important to have him for the rest of the season," Guillen said. "That's why we really put attention on it. It's not that bad. You just make sure he's in the right place. ... We will take a real close look at it and make sure he'll be fine."
And Guillen said if the groin is an issue at all, there is no way Thome will go in the field at first base for the first time this season when the White Sox play interleague games in National League parks.
"He was taking ground balls, and if that's going to hurt him, he's not playing," Guillen said.
The White Sox's first interleague road game is June 16 at Cincinnati, and Thome hopes he'll be ready.
"The main thing is to focus and do the treatment and get back as quickly as possible," Thome said. "It's important to get it done now, get it cleared up and get it going and when we do get in those interleague games, I can play out there."