All passengers alighted from the Free Bird airline Airbus A320 safely and the man was arrested after the incident on Tuesday night.
A spokesman for the Bavarian police, Armin Ganzerer said a 28-year-old Turkish man had been arrested and was being treated in hospital. His motives were still unknown.
"A few minutes after the landing a person threw himself from the plane and was injured," he said. "That person was the assailant."
Special police units searched the plane but found no bomb.
The police spokesman said the plane had taken off on schedule shortly before 9pm (1900 GMT) and that a man had made a bomb threat to a crew member.
He said the pilot then returned to the airport and landed the plane 43 minutes after take-off in Munich, southern Germany.
The passengers and crew left the plane by stairs and were transported to an airport departure hall where they were questioned by police.