Messi was taken to the clinic at Barcelona's training ground and the club are hopeful that the injury was nothing more than a "hyper-extension" around his right elbow.
'Psychologically we know that when he is there we are stronger but we can not allow his absence to affect us, ' centre back Pique said after the game.
"In the past we have had games without him and we have always tried to maintain our style".
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He was still in obvious discomfort as he left the field in the 26th minute but there was no blamed attached to the Italian as he competed fairly for the ball, but Messi's full body weight landed on his right arm.
"What happens is that people want to put me in confrontation with Messi and they can't". "We have a team good enough to do well in the matches that we have ahead".
Messi scored the team's second goal with a shot from outside the area in the 12th.
Barcelona are all set to host Inter Milan in their UCL fixture on Wednesday, but Messi's injury means the Italians will not be able to go up against the five-time Ballon d'Or victor.
After Sunday's clasico, Messi also stands to miss a Copa del Rey match against Cultural Leonesa, the return leg against Inter and league contests with Rayo Vallecano and Real Betis leading up to the next global break.
Julen Lopetegui's club dropped another result on Saturday, falling 2-1 to Levante, and sit fifth in the league table, four points back of Barca.