Wenger lost another defender, Kieran Gibbs, for three weeks to a thigh injury during the 2-2 draw with Liverpool - a game during which the Gunners displayed the defensive frailties that have blighted them all season.
Wenger's response was to do an out-of-character piece of late business, paying an undisclosed fee for 26-year-old Spain international Monreal as the clock struck 11.
"We are delighted that Nacho Monreal has agreed to join us. We have been monitoring him for some time now and are really pleased that we've been able to agree this move today [Thursday]," Wenger said.
"Monreal is a strong left-sided defender with good experience at both club and international level. He is a technically gifted player, a good crosser in the final third and strong in the air.
"He will add quality to our squad and of course, to our defensive unit. We all look forward to him playing for us."
The deal remains subject to the completion of what the club describe as a formal registration process, but does represent an unusual move from Wenger.
He has rarely dealt so close to the deadline, but the injury suffered by Gibbs last night seems to have forced his hand.
Monreal, a former Osasuna academy graduate, signed for Malaga for £6million in 2011 after making an impression with his hometown club, for whom he made 127 appearances.
He made his debut for Spain in a 2009 friendly against Macedonia and has gone on to win nine caps for the national side.
He should add some steel to a much-maligned Arsenal back four - a defensive line that was bailed out by Olivier Giroud and Theo Walcott against Liverpool.
They made a number of catastrophic errors and were fortunate to only be 2-0 down when the comeback started, and according to striker Lukas Podolski, they cannot keep letting teams get a jump on them.
"It is a problem in the last matches that we are losing a goal and then coming from behind," the German said.
"We must start strong from the first minute and score the first goal.
"In the last few weeks that has always been the problem, that we have to fight and come back.
"However, when you are 2-0 down and you come back like against Liverpool it feels like three points, and this is the way we have been playing recently."
Arsenal remain sixth, four points behind Tottenham and three off fifth-placed Everton in the race to secure Champions League qualification once again.
Podolski, though, insists the team have what it takes to overhaul their rivals and even catch third-placed Chelsea, who have an eight-point advantage over Arsenal.
"We must fight for the Champions League places and this is our focus. We want third place and we have a lot of matches to play," he said.
"We are in the FA Cup and the Champions League, but the focus must be on the Premier League.
"Of course we wanted to finish first, but we lost a lot of points in the first half of the Premier League and now the difference is too big.
"All the other teams are really strong so we must fight in every game."