The individual, aged 32, is believed to be a resident of one of the flats on the 11th floor. At the time of detention, the man was highly intoxicated with alcohol.
He was arrested for 48 hours and will face allegations of arson.
The police are carrying out an investigation into damage of property in a generally dangerous manner, a crime punishable by a fine, restriction of freedom, arrest or a custodial sentence of up to five years.
Firefighters evacuated 76 residents from the building. Medics checked 9 people on site. People were temporarily placed at a nearby vocational school.
The fire was put out at 1 a.m., the premises were aired and people were allowed to return to their homes.
The fire destroyed a flat on the 11th floor, walls in the stairway were covered in black soot and water damaged flats below. Windows of a flat above cracked.