Varane was substituted at half-time during the LaLiga encounter, the France international having to watch the remainder of the game from the stands as Madrid were thrashed 5-1 at Camp Nou.
The loss brought the end of Julen Lopetegui's reign at the Santiago Bernabeu, the head coach sacked on Tuesday after failing to deliver the results with a star-studded Madrid squad.
FIFA World Cup winner Varane is one of many Madrid players to have under-performed this season, the 25-year-old having featured in nine of its 10 league matches.
He could miss this weekend's clash with Real Valladolid, though, after sustaining a muscle injury against Barca.
A brief statement read: "After the tests carried out on Raphael Varane by the Real Madrid medical services, he has been diagnosed with a muscle injury to the adductor in his right leg.
"The player's situation will continue to be monitored."
Mariano Diaz, who played the final eight minutes of the Clasico, will also be monitored after being diagnosed with a thigh injury.