During an interview outside the museum on Monday, a tile fell from a height of around 12 metres, landing very close to the PM, who was speaking to broadcaster TV2 at the time.
TV2’s reporter Sverre Quist said the tile landed around one metre from Rasmussen.
Journalist Cathrine Bloch of Berlingske, who was also present, wrote on Twitter that the incident looked “seriously insane”.
Rasmussen has in the past specifically mentioned being “hit on the head by a roof tile” in reference to contingency planning for his succession in an emergency, according to Bloch.
A visibly shake PM was immediately taken to safety by police security personnel after the tile hit the ground, TV2 writes.
He was able to comment on the incident shortly afterwards, however.
“I think we all had a shock there. But I was fortunately not hit on the head by a roof tile,” he said to TV2.
“We have things under such control in the Liberal party that we’d know what to do if I were hit on the head by a roof tile,” he added afterwards.
“For just a split second, you think, ‘you never know’. It’s a small reminder that nothing should be taken for granted in life,” he said.
Nobody was injured due to the incident, TV2 reports. The National Museum is looking into the cause of the falling tile, but renovation is not to blame, the cultural institution’s head of communication Jacob Frische said to the broadcaster.