Arsenal boss Wenger, a former manager at Monaco, is now facing elimination at this stage of the competition for the fifth straight season after the shattering home defeat.
French midfielder Geoffrey Kondogbia put the visitors ahead after 38 minutes, when he crashed in a long range shot that took a deflection off Arsenal defender Per Mertesacker, leaving goalkeeper David Ospina helpless.
Bulgarian veteran Dimitar Berbatov, continually jeered by the home fans because of his past links with their arch-rivals Tottenham Hotspur, added the second after 53 minutes after a devastating Monaco counter-attack.
Arsenal pulled one back in stoppage time when substitute Alex Oxlade-Chamberlain curled home from the edge of the area, but Monaco scored even later to restore their two-goal advantage when substitute Yannick Ferreira-Carrasco scored with a shot that went in off the post.
Arsenal wasted several chances with Olivier Giroud spurning four scoring opportunities to leave Arsenal with a mountain to climb when Wenger takes his side back to the principality for the second leg on March 17.
ROCK SOLID
Wenger's Arsenal, who had won eight of their last nine matches in all competitions, flew out of the blocks against his old team, testing the resilience of Monaco's rock-solid defence with a series of early raids.
Giroud went close with a header during Arsenal's opening dominant spell, and then wasted three chances after the break before being substituted, but Monaco weathered the early storm, subduing both the crowd and the home players.
The visitors gradually played their way into the match with winger Anthony Martial and Joao Moutinho looking particularly dangerous, but it was still a surprise when they took the lead through Kondogbia's long-range effort.
There was no real surprise, however, when they doubled their advantage as they were playing the better football when Berbatov's powerful finish ended a swift break.
The hosts were given a lifeline in the first minute of stoppage time when Oxlade-Chamberlain pounced on a clearing header before curling home, but their celebrations were short-lived as Ferreira-Carrasco finished emphatically.
Monaco had scored only four goals in their six group stage matches and it was not hard to see why as Brazilian defender Wallace and Tunisian Aymen Abdennour were towers at the back.
Arsenal have shown plenty of resilience themselves over the years to come back against the odds, but will have to surpass themselves to save the tie now.
(This version of the story refiled to add word European in first para)
(Editing by Toby Davis)
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