The Frenchman has come in for a lot of criticism in recent days as the Gunners lost 1-0 to Championship side Blackburn Rovers in the FA Cup on Saturday, before being defeated 3-1 by Bayern Munich in the Champions League last night.
Those results have meant that Arsenal's wait for a trophy under Wenger's guidance is likely to enter into a ninth year.
However, despite the negativity that surrounds the Emirates Stadium at the moment, Vermaelen has urged the club's board to stick by their manager.
"Of course we're behind him. He's done a lot for this club. He still does a lot of hard work with us. He is the right man for the job," said the Belgian defender. "We have to show it on the pitch as well. At the moment the results are not good. But we will work hard with him to get the results back.
"Everyone in football looks too short term. They don't look at the long term and he's done a lot for this club. It doesn't mean that because it's not going well at the moment we don't stand behind him.
"You have to look at the long term. He is the right man for this club and we are all behind him."
Wenger, 63, took charge of Arsenal in August 1996.