The 24-year-old Munich man was arrested by the city's airport police on December 30th. It is not clear if he was intending to board a flight, as he was arrested while sitting in one of the airport restaurants.
He was kept in custody on New Year's Day and police said in a statement on January 1st that the man had admitted to arson.
"The motive for his act was relationship problems," the statement said.
Alarmed neighbours also living in the building in Neuaubing, a suburb the Bavarian capital noticed a burning smell at 8pm and called the police.
Everyone managed to get out and no-one was injured.
Damages are thought to amount to around €40,000 and the burnt-out building is inhabitable.