"Sergio's injury looks like a strain and we hope that's all it is but the doctors are the ones who have to determine what it is. He's a very important player for us and his club," the coach told a news conference.
Ramos will undergo further tests when he returns to the Spanish capital on Monday to determine the extent of his injury.
Although Ramos has endured a stumbling start to the season, conceding four penalties for club and country, his absence will be keenly felt by Real and coach Zinedine Zidane, who has recently been without Brazilian duo Marcelo and Casemiro and midfield maestro Luka Modric.
The former Real great has also faced serious criticism for the team's stuttering run of four consecutive draws in all competitions, which culminated in a shock 1-1 draw at home to Eibar last Sunday.
Ramos is likely to miss Real's La Liga games against Real Betis, Athletic Bilbao, Alaves and Leganes and two Champions League group games with Legia Warsaw.
He is also doubtful for Spain's World Cup qualifier with Macedonia on Nov. 12 and friendly versus England on Nov. 15.
If his recovery goes according to plan, the 30-year-old will return to action in time for the Madrid derby against neighbours and La Liga leaders Atletico Madrid on Nov. 20.
Marcelo is set to return from his calf injury to face Betis on Saturday but Casemiro, credited with balancing the team last season and helping Real set a joint record 16 straight league wins, is not due back until the end of October as he recovers from a fractured fibula.
Real's Croatia midfielder Modric, nursing a knee problem, is not expected to return until the start of November.
(Reporting by Richard Martin; Editing by Ken Ferris)
