Real Madrid remain unbeaten this term, having now won five and drawn one of their first six matches in all competitions under returning coach Carlo Ancelotti
His second tenure was fraught with tension, which came to a head in an unusually fiery press conference in February when he demanded more respect for his team.
The one marquee signing the club made in Zidane's second spell was Eden Hazard, who has been unable to shine due to a hapless run with injuries.
The Frenchman, who has won three Champions League trophies and two La Liga titles in two spells as Real coach, could find his future under threat should Real end the season trophyless.
"Let's just finish this season. What I will say is that I'll make things easy for the club, always, because they've always given me everything," Zidane told a news conference on Saturday.
Local media reported that the defender could miss the European fixture next Wednesday as well as the La Liga title run-in as Real attempt to defend their league crown.
Real, who sit two points behind league leaders Atletico on 71 points and face Osasuna on Saturday, have not put a timescale on Carvajal's return.