The defender lasted 38 minutes of the 3-2 win over BVB in the Champions League clash and is now a huge doubt for the La Liga showdown with Sevilla this weekend.
Varane was able to walk off the pitch, but it still looks to be a muscular injury and is the last thing Zinedine Zidane needs right now.
Real are already missing suspended trio Sergio Ramos, Dani Carvajal and Casemiro, while Cesar Vallejo is injured.
“He hurt himself and we will see. Tomorrow [Thursday] they will do a scan. The player is optimistic but he will not be available on Saturday, that’s for sure,” said Zidane.
It means midfielder Marcos Llorente may have to slot into the back four at the weekend.
“It could happen,” Zidane added. “He already knows that position. He played it for Castilla some times.”
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.