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At least one person’s death was believed to be connected to the explosion at a residential building early on Wednesday, which Munich police said was deliberately set on fire and part of a domestic dispute.
It was not immediately clear whether the deceased was the suspected perpetrator or someone else.
Another person, who was not considered to be a danger to the public, remained missing.
Specialised teams were called to the scene to defuse booby traps in the building, police said. Photos from the area also showed a burned-out van.
Officials discovered the bomb threat to Oktoberfest in a letter from the alleged perpetrator.
Police searched the fairgrounds for other explosive devices and asked workers to leave the area.
Authorities said the festival would be closed at least until 5pm on Wednesday (1am Thursday AEST).
This year’s Oktoberfest began on September 20 and ends on October 5. The world’s largest beer festival usually attracts up to six million visitors.
In 1980, Oktoberfest was the target of a deadly neo-Nazi attack. The bombing on the evening of September 26, 1980, claimed 13 lives, including that of three children and the attacker, student Gundolf Koehler, a supporter of a banned far-right group. More than 200 people were wounded.