The plane was travelling from Alicante to Liverpool when the man was detained by police at Liverpool John Lennon Airport yesterday.
Officers were called to the airport in response to reports that a male passenger was being disruptive on board, the Liverpool Echo reported.
The man was from West Derby in Liverpool and was arrested on suspicion of being drunk on an aircraft and has been taken in for questioning, they said.
According to an eyewitness, the man allegedly "belched at another passenger and then fell onto a small child".
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"She asked him to stop but when he wouldn't. She had to ask the cabin crew to get involved. By that point we'd started to land and the seatbelt signs were on but he stood up and started mouthing off," the passenger said.
"When we landed there was a police van and two officers waiting to arrest him," he added.
Ryanair has condemned the man's behaviour and said they "do not tolerate unruly or disruptive behaviour at any time".