Oduya's scratch marked the first regular-season game he's missed for the Blackhawks since being traded to the team in February 2012, a span of 124 consecutive games.
Blackhawks coach Joel Quenneville described Oduya, selected to play for Sweden in the Sochi Olympics, as being day-to-day.
"I don't think it's going to be a problem for him in the Olympics," Quenneville said after Wednesday's game. "I think we're being safe for that with him. We'll see how he presents [Thursday].
Oduya played just shy of 19 minutes against the Los Angeles Kings on Monday.
Oduya has three goals, 10 assists and a +7 rating in 58 games this season.
Oduya is questionable to play against the Phoenix Coyotes on Friday. He will be re-evaluated on Thursday.