As outlined by a report in Marca, the Spaniard is set to be out of action until after the next international break after sustaining the injury in Saturday’s El Clasico victory over Barcelona.
Nacho had to be withdrawn minutes before half-time and was replaced by Lucas Vazquez, who is now likely to deputise in the position for the next run of fixtures.
Madrid take on Borussia Monchengladbach in the Champions League this midweek in the midst of a busy run of fixtures.
Nacho is naturally a central defender but had been deputising at right-back in the absence of the two first-choice players in the position.
Carvajal has damaged the internal lateral ligament of his right knee, in news that means he also missed out on a call-up to the Spain squad for the recent international break.
Alvaro Odriozola is also currently unavailable for Los Blancos due to injury, while first-choice left-back Ferland Mendy deputised in the position against Shakhtar Donestk last week in the Champions League.