Jose Mourinho, seeking a third Champions League winners' medal, saw his Madrid side paired with surprise Cypriot package APOEL Nicosia, who came through a group including Porto before eliminating Lyon in the last 16.
Holders Barcelona, meanwhile, face a rematch with Italian league leaders AC Milan, with the duo having already met in this season's group phase. Milan held Barca to a 2-2 draw at the Nou Camp before goals from Xavi and Lionel Messi helped seal a 3-2 win for Pep Guardiola's outfit at the San Siro.
England's only remaining representitives in Europe, Chelsea, face Benfica, who helped oust last year's runners-up Manchester United in the group stage.
While Bayern Munich, hoping to reach the final to be played in their own stadium, will fancy their chances of reaching the last four against a Marseille side struggling domestically.
The winners of the tie between APOEL and Real Madrid will face the victors of the Marseille-Bayern Munich clash in the semi-finals, with Benfica or Chelsea coming up against either AC Milan or Barcelona for a place in the Allianz Arena showpiece.
"If you want to be champion of Europe you have to beat the best and Milan is without doubt among them," Barca coach Pep Guardiola told reporters in Spain.
"Milan have seven European Cups on their curriculum, all their players are of exceptionally high quality and it will be a very tough tie.
"They are an excellent team in every way, very strong defensively and with quality in midfield and up front that is extremely high. Their players have come through a great number of battles and they know what they are about."
Led by 12-goal Lionel Messi, the Catalans will visit San Siro for the first leg on March 29 as they continue their attempt to become the first side since Milan in 1990 to defend their European crown.
Milan director Umberto Gandini told reporters: "It was pretty much evenly balanced when we met in the group stage.
"We drew away and we lost in Milan with a strange penalty, I know they will not be happy to play us."
Milan striker Zlatan Ibrahimovic's return to Nou Camp, which he left in acrimonious circumstances, will add further spice to the meeting.
TOO FRENZIED
APOEL have already surpassed expectations by becoming the first Cypriot team to reach the last eight and Erotocritou was reluctant to predict an even greater upset than their round-of-16 elimination of Olympique Lyon.
"We have beaten teams like Zenit [St Petersburg], like Porto, we will try," he said. "I know chances are minimal but we have got quality players and we will give it a try.
"It has been a fantastic dream but maybe the dream is getting near to the end."
He said record nine-times winners Real would face an atmosphere in the first leg in Nicosia that even APOEL officials found too frenzied.
"Unfortunately,
