He will be re-evaluated in four weeks, the team said.
At 12:59 of the first period, San Jose's Logan Couture pushed the puck past Elliott for a power-play goal that gave the Sharks a 3-0 lead.
There was a jumble of bodies in front of the net on the play. Elliott went down to block the shot, and the puck squirted past him.
After Blues trainers came out, Elliott left the ice and went to the locker room.
Jake Allen replaced Elliot and finished with 15 saves. The Blues activated Allen from injured reserve Sunday.
Allen sustained a lower-body injury during the team's game Jan. 8 against Anaheim and had missed 17 games.
"I haven't played in a month and a half," Allen said. "I got my feet wet. We got too far behind the eight ball to catch up."
The Blues were able to withstand Allen's injury, going 12-3-2 during his absence thanks to Brian Elliott's stellar play in front of the net.
Elliott, 30, recently had a streak of three straight victories in which he allowed only one goal (Feb. 14-18). According to ESPN Stats & Information, it's the second time this season that a Blues goaltender had won three consecutive games while allowing no more than one goal in each game. Allen, 25, accomplished the feat in a stretch of games Nov. 4-10.
Elliott is 17-7-6 this season with a 2.14 goals-against average, a .929 save percentage and one shutout.
Allen has an 18-11-3 record this season with a 2.18 goals-against average and .923 save percentage. He has five shutouts this season.
The Associated Press contributed to this report.