Premier League - Video: Man handcuffs self to post
The spectator attached himself to City goalkeeper Joe Hart's left-hand post five minutes before half-time at Goodison Park.
He appeared to be protesting against Ryanair, as he wore a t-shirt criticising the airline's wages and recruitment policy.
Both teams' managers used the pause to speak to their players as several Merseyside Police officers worked to remove the man from the post.
In a statement, Everton said: "Bolt-cutters were used to remove the offender, who was roundly booed as he was escorted from the ground.
"It transpired that the supporter is a known professional protester, allegedly protesting about an airline's recruitment policy. He was arrested by Merseyside Police, who are now dealing with the matter."
Merseyside Police said a 46-year-old man from Southport was arrested for pitch invasion following the incident.
A spokesman added: "He has been taken to a police station, where he remains, to be questioned."
Everton went on to win the match 1-0 thanks to a Darron Gibson goal.