Brodkin, best known for his creation Lee Nelson, stretched and took part in exercises with the team for five minutes before being noticed.
His spokesperson said to the Daily Mail: "Simon was doing some meetings with fans on the street and having pictures taken as his football character Jason Bent for his Facebook page.
"He was then going to see the game as he's a big Manchester City fan and I think the prankster in him couldn't resist."
Brodkin was wearing identical kit to the players and was heard shouting, "'Come on, let me play. I've got 50 grand on me to score first" as he was escorted out.
An Everton spokesman said: "A man, believed to be from the London area, has been arrested by Merseyside Police for pitch encroachment."
Twitter user AntonyEvans_98 later uploaded a photograph of Brodkin talking to police, writing: "Lee nelson getting arresting for trying to be a city player haha quality!"
Brodkin was previously arrested in November 2012 in the guise of Lee Nelson, after pretending to steal a copy of his DVD from an HMV store in London.