Simon Brodkin, who performs as the character Lee Nelson, was taken away by police from the headquarters of football's world governing body after Blatter's security escorted him out of the press conference room where he carried out the stunt on Monday.
“He was arrested and interrogated by the police,” a spokesman for the Zurich police said, without identifying Brodkin, who has been involved in previous stunts, by name.
“There is a possible complaint about trespassing. We don’t know if there will be a trial or not, that is to be decided by the prosecutor and that will take some time."
The spokesman added that FIFA had made a complaint to the police about the incident.
FIFA was not immediately available for comment.
Dan Lloyd, a spokesman for Brodkin's agents Avalon, said the comedian was back in Britain and had not been held overnight by Swiss police.
Brodkin has been involved in similar stunts in the past, including going on stage with rapper Kanye West at the Glastonbury Festival and, in 2014, attempting to infiltrate the England World Cup squad as they flew to the United States.
In 2013, Brodkin found himself in a British court after another football-related prank.
Dressed in full football kit, in the guise of another of his characters, footballer Jason Bent, Brodkin warmed up on the field with Manchester City players before their game at Everton's Goodison Park.
The comedian was charged with entering the playing area under the Football Offences Act but was let off with a caution in court.
(Reporting by Simon Evans and Joshua Franklin; editing by Justin Palmer and Ken Ferris)
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