Wenger faced questions about his future after Arsenal lost to City in the EFL Cup Final on Sunday and this defeat will lead to more calls for him to be sacked.
Arsenal were ripped apart at Emirates Stadium and were 3-0 down at half-time after Bernardo Silva, David Silva and Leroy Sane scored for City.
Wenger insists he will not walk away and intends to honour his two-year contract, but this was another crushing defeat against the argument for him to stay in charge.
City were on a different level to Arsenal and this match again demonstrated how far the Gunners have fallen under Wenger.
The result leaves Arsenal 10 points outside the top four and surely ends their already slim chances of finishing in the Championship League places.
City extend their lead at the top of the Premier league to 16 points.
Arsenal had actually started well but they fell behind after 15 minutes thanks to a wonderful curling effort by Bernardo Silva and things quickly got worse.
City scored a second goal on 29 minutes when the Arsenal defence was ripped apart and David Silva finished off a brilliant team move.
It was irresistible football and Arsenal were three down on 33 minutes when they were carved open again and Sane tapped home a cross from Kyle Walker.
Arsenal fans started heading for the exits and a chorus of “you’re not fit to wear the shirt” greeted the half-time whistle.
Things could hardly get much worse for Arsenal but they did at the start of the second half when Pierre-Emerick Aubameyang had a penalty saved by Ederson.
City did not have to get out of second gear after that and cruised to an easy win that leaves Wenger facing more questions about his future.