Defending champion Madrid will play Schalke a year after a 6-1 rout in Germany sparked a 9-2 aggregate victory.
"We want to show that we've learned something," Schalke coach Roberto Di Matteo said. "We got the toughest rival."
Barcelona will once again travel first, on Feb. 24, to play Manchester City. Barcelona beat City 4-1 on aggregate at the same stage last season.
"We have tried to improve at the back. We are more solid than last season," said Man City director of football Txiki Begiristain, a former Barcelona player and director. "The only reason to be happy is that I can go home."
The draw also paired Wenger with former team Monaco, where the Arsenal manager rose to prominence by winning a French league title in 1988.
"It's AS Monaco - Mon. Wenger will be happy about the draw," Arsenal playmaker Mesut Ozil wrote on his Twitter account.
More repeat business will see Paris Saint-Germain again host Chelsea first, after the English club advanced from their quarterfinal series last season.
"What happened last year was a good experience that shall not be repeated," PSG president Nasser Al-Khelaifi said.
Bayern Munich, which won the most recent of its five titles in 2013, will be away first against Shakhtar Donetsk. The runaway Bundesliga leader has never played the Ukrainian champions.
"Donetsk is a big unknown for us. It won't be so easy to prepare for these matches," Bayern goalkeeper Manuel Neuer said.
Shakhtar, which is based near Ukraine's eastern border with Russia, is scheduled to host its match on Feb. 17 in Lviv because of the ongoing conflict in its home city with separatist forces.
Juventus will face Borussia Dortmund in a repeat of the 1997 final which produced one of the biggest Champions League upsets. Back then, Dortmund beat the heavily favoured defending champions 3-1.
Also, Bayer Leverkusen will face Atletico Madrid, and FC Basel will play FC Porto in a match of clubs which sustain good Champions League results despite often selling star players.
"Every year they sell wonderful players at high prices and they stay sportively on a very high level," said Basel club president Bernhard Heusler, whose team ousted five-time champion Liverpool last week. "We have no fears, only a lot of respect."
The first legs will be played on Feb. 17-18 and 24-25, with the return matches on March 10-11 and 17-18.
The final is scheduled for June 6 at the Olympic Stadium in Berlin.
AP Sports Writers Nesha Starcevic in Frankfurt, Germany, and Samuel Petrequin in Paris contributed to this report.