Ramos' injury was confirmed after Saturday's goalless draw against Atletico at the Wanda Metropolitano.
Although Madrid or boss Zinedine Zidane did not disclose how long they expected Ramos to be absent, the 31-year-old did not feature in the European champions' 20-man travelling party for the game in Cyprus.
Once again, there was no place for Gareth Bale or Keylor Navas.
Bale is recovering from his latest injury setback, a groin strain suffered earlier this month, while Costa Rica goalkeeper Navas is back in training following an abductor tear but not yet deemed ready for action.
Madrid are looking for a return to winning ways in the Champions League after taking a solitary point from back-to-back encounters with Tottenham in Group H, although a draw would be enough to seal a place in the knockout stages in the event of Borussia Dortmund failing to beat Spurs at Signal Iduna Park.
Zidane's men have only won one of their past four games in all competitions.