"He's got a little bit of an upper-body issue, day to day," Blues coach Ken Hitchcock said.
The Blues had two on-ice sessions Tuesday, and Elliott didn't come out for the second one.
"Rather than just try to squeeze the big, long (practice), we took him (out after) the short one and we'll get him back out here tomorrow or the next day and see how it is. He'll be fine though," Hitchcock said.
"We didn't want to aggravate it. We've been nursing it for a week. We didn't want to take him too far down the lineup. He got a lot of work in the first 45 minutes."
Elliott, who didn't speak to reporters Tuesday, led the NHL this season with a 1.56 goals-against average and a .940 save percentage.
Hitchcock has not yet tipped his hand on which goalie would start Thursday night in Game 1 against the San Jose Sharks. Jaroslav Halak is the other part of the league-leading tandem that allowed the fewest goals this season.
Hitchcock said he would announce his starter Wednesday.