European police said on Monday that about 680 suspicious matches, including qualifiers for the World Cup and European championship and the Champions League, had been identified in a match-fixing inquiry.
Wenger said he doubted the problem extended to sport in England.
"I personally feel English football is clean of cheating 100 percent," the Frenchman told reporters in his pre-match briefing on the eve of Arsenal's visit to Sunderland in the Premier legue on Saturday. "I don't think referees are corrupt.
"In sport in general, I don't think at all it's a problem in the English game," he added. "That's why it's maybe a shock for us because we are convinced we live in a world in England where it's not a perfect world but I don't think cheating or match-fixing is a problem.
"It happened in Europe before, that is my belief, where referees were not always fair, especially in some countries. But you always have to be cautious, have your own beliefs, prove it, and that becomes more difficult."
Wenger said it was time to tackle the problem "in a serious way" because "sport is full of legends who in fact are cheats".
Referring to the findings of the European police match-fixing inquiry he added: "It was absolutely a surprise... the number of games that have been fixed.
"I can't accept it and I always was a believer that there's a lot of cheating going on in our game and that we are not strong enough with what happens, nor with the doping, nor with the corruption of the referees, nor with the match-fixing.
"It's time that we tackle this problem in a very serious way and that people who cheat are punished in a very severe way as well."
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