The Belgian has found first-team opportunities hard to come by in recent months but his boss wants to see him take the chance created by Laurent Koscielny's injury
Vermaelen started his first league game since December in Tuesday's 2-2 draw with Swansea due to Laurent Koscielny being absent with a calf strain.
The Belgium defender was a first-team regular last season but has struggled to displace Per Mertesacker and Koscielny at the heart of the Arsenal defence this term, and as a result has only started four league matches.
With Koscielny expected to be out for a couple of weeks Wenger has backed Vermaelen to prove his worth.
"We know Thomas has paid a heavy price for having Laurent and Per who worked well together," the Frenchman told Arsenal's official website.
"But he has an opportunity to show how good he is and I'm sure he will take it."
Vermaelen is expected to start against Manchester City on Saturday as Arsenal look to avenge the 6-3 defeat they suffered at the Etihad Stadium.