The Frenchman fears the lack of money at lower levels of the game could encourage illegal activity.
Six people were arrested this week on suspicion of being members of an illegal international betting syndicate based in Singapore, and two men appeared in court in Cannock on Friday.
Wenger believes the lower levels of the English game may always be vulnerable to those looking to manipulate matches.
“Can it be eradicated completely? I’m not sure,” he told reporters. “Is it a concern for me and you who love the game? Certainly yes because it is not only a concern for me, it is [also] a shame. Once you don’t know anymore if everyone is genuine out there, that is something absolutely disastrous.
“I think we have to fight against that with the strongest severity to get that out of the game. Maybe the lower divisions are a bit more under threat because it is a bit more anonymous, there is less money so it is easier to buy people. But I don’t think that exists in the Premier League at all.
However, the Arsenal manager does not believe match manipulation is indigenous to the UK.
“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. It’s a new problem that we all face. I still think that 99.9 percent, the English game is completely clean. I hope that’s an isolated incident.
“When you see the happiness of the players when they score goals, even in the lower divisions, the passion of the fans when I was at Barnet, for example, I can’t believe there is a matchfixing problem in England.”
Speaking on the same subject, Chelsea boss Jose Mourinho added: “Match fixing is something that doesn't come into my brain, I can't understand how it's possible.
“I feel we are all in love with the game... football is the kind of job you go into it because in love with it.”