Hudson, who had X-rays which came back negative, was forced to leave Chicago's 9-5 victory in the sixth inning and was not expected to play in Thursday's series finale.
"He could probably go in if he was going to hit right-handed," White Sox manager Robin Ventura said about the switch-hitter. "Not going to run too much. He's pretty sore, I would imagine I can't use him tonight."
The injury didn't completely dampen Hudson's return to Toronto, the place where he began his Major League career.
Hudson, who was a member of the Blue Jays from his rookie season in 2002 until '05, said he always enjoys playing in Toronto and catching up with old friends.
"It's always fun to come back here. I consider it like home," Hudson said. "It was my first team. I always enjoyed it here. It was a blast here.
"Lots of great people, I met a lot unbelievable people, great organization and I had a lot of fun here."
Hudson's fondest memories of playing in Toronto came when the Blue Jays would square off against the Yankees and Red Sox, a pair of division rivals, because of the atmosphere and increased attendance when those two clubs were in town.
The 11-year veteran had nothing but positive things to say about his time in Toronto, but added that he is very happy to be a member of the White Sox.
"We have a great chemistry in the clubhouse and off the field," Hudson said. "This is a team that gets along, we have a lot of fun, a great coaching staff. Everybody laughs and talks but we take the game seriously."