Two men with Singaporean nationality suspected of fixing matches in lower-league English football were remanded in custody by magistrates on Friday.
The men, alleged to be members of a Singapore-based betting syndicate, were among seven people arrested this week in an investigation by the National Crime Agency (NCA).
Wenger saw at close quarters the damage match-fixing can do during his time in charge of Monaco when French champions and 1993 European Cup winners Marseille were found guilty of corruption, relegated and banned from European competition by UEFA.
"Can it (fixing) be eradicated completely? I am not sure. It is not only a concern for me, it is a shame," Wenger said. "Once you don't know if everyone is genuine out there any more, that is something absolutely disastrous," the Frenchman added. "I think we absolutely have to fight against that with the strongest severity to get that out of the game."
Wenger was confident the huge wages on offer to players in the Premier League were a deterrent to fixing, although he accepted there could be a problem in English football's lower divisions.
"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," he said.
Wenger, in charge of Premier League leaders Arsenal since 1996, added: "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 any more.
"It is a new problem that we all face. "I still think that 99.9 percent, the English game is completely clean." And he stressed that comparisons between current issues and those that engulfed Marseille were misplaced.
"That was much more serious," he said. "It was a period where European football was not clean, for different reasons, but I hope we have that behind us. "Personally, it was one of the most difficult periods in my life, but I think even in France now, the championship is completely clean."
Ar the time of the Marseille scandal, Wenger was making his name as a manager and he said the furore had shaken his self-belief.
"You know what it is when you're in a job like mine. You worry about every detail, about who to pick for the next game, to prepare the next game, and when you go to the game and you know all that is useless, it is of course a disaster. "I always felt that in the end the game will come clean again and the love for the game from everybody will take over."
Wenger added: "In that case, all the rest of the people are responsible for what they do and during all that period I can look back and say I behaved always like I wanted - what other people did is their problem."