The issue has come under the spotlight on British shores after six men were arrested on allegations of being involved in an illegal betting syndicate.
"I don't believe that in England people fix matches, but we live in an international world and you cannot just stop it at the border anymore," Wenger said in a press conference. "It's a new problem that we all face.
"I still think that 99.9%, the English game is completely clean. I hope that [the recent charges] is an isolated incident.
"Can it be eradicated completely? I'm not sure. Is it a concern for me and you who love the game? Certainly yes because it it is not only a concern for me, it is a shame."
A seventh man was arrested by the National Crime Agency yesterday, but he and four others were released on bail pending further enquiries.
Two men have been charged by police and will remain in custody until December 13.