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 champion's 20-man travelling party for the game in Cyprus.
They are also fresh from big wins in their last two league games after a slow start to their Cypriot title defence.
On paper, 12-time European champions Real are overwhelming favourites against an Apoel side that are without a win in their last 12 matches in the Champions League proper, and who are now only fifth in the Cypriot top flight.
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Speaking to reporters ahead of the match, Zidane said: "He [Benzema] is the first one who knows he can give more, because of the confidence issue, especially his confidence in front of goal". Despite domestic competitions being hotly contested across Europe, it is the Champions League that most teams want to win, with a place in footballing immortality awaiting the victor.
Ramos' injury was confirmed after Sunday's goalless draw against Atletico at the Wanda Metropolitano.
Though beaten by 3-0 by each Real and Tottenham Hotspur previously, APOEL have better results on home soil as they drew 1-1 twice with Borussia Dortmund.
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Among the criticisms levelled at the Real is the performances of star forwards Cristiano Ronaldo, Karim Benzema and Gareth Bale, with the trio having scored just four LaLiga goals between them this season.
Scroll through the gallery above to see how Real Madrid could line up against Apoel Nicosia.
'They deserve to be in the Champions League and when they came to the Bernabeu they played very well. "Let's hope tomorrow [Tuesday] is the day to end the streak".
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Real will be without Bale and goalkeeper Keylor Navas once again, while captain Sergio Ramos is unavailable after breaking his nose in the derby.
"Strange as it may seem, we are not impressed".
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The 28-year-old also indicated that the next step in his recovery process will center on cutting and changing direction.