The police have received five reports from the Cyprus Football Association (CFA) regarding suspect games and have said they are determined to stamp out the phenomenon.
The footballer is reportedly a player from a second division team based in Limassol.
The arrest follows the CFA saying on Saturday that Uefa has accepted its request to dispatch a team to the island over the ‘red notices’ it sent on suspicious betting activity that could mean match fixing.
The issue was discussed on Friday at a meeting at the justice ministry following a bomb attack against a football referee in Larnaca earlier in the day.
The Uefa team will cooperate with the police to investigate the matches for which the European football governing body issued the notices, over suspicion of foul play. They will also train representatives of football clubs on how to deal with them.
Over the coming days players, coaches and others are expected to be questioned.