Vazquez had to come off before half-time in the 2-1 win over Barcelona but not before he had crossed to Karim Benzema to score the first goal.
Real announced the player was suffering from a left knee ligament sprain with the Spanish media suggesting he could be out for the rest of the season.
The first match he will miss is Wednesday's Champions League quarter-final second leg with Real travelling to Anfield with a 3-1 first leg lead.
His absence adds to Zinedine Zidane's injury concerns with Sergio Ramos, Raphael Varrane and Dani Carvajal all sidelined for the game.
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