A sperm whale has died in Western Australia days after it was filmed in shallow waters among dozens of delighted beachgoers, authorities have said.

Curious swimmers paddled out to stroke the 30-tonne mammal after it was spotted close to shore south of the state capital Perth over the weekend.

But wildlife officers urged crowds to stay away from the 15-metre whale, saying it was clearly sick and dying.

"It is really unusual for a sperm whale to be anywhere near these metropolitan waters," incident controller Mark Cugley said on Tuesday afternoon after confirming the whale had died.

"We don't really know why, it is very unusual. It is obvious that it wasn't well."

A traditional Aboriginal smoking ceremony was held on Tuesday evening to bid farewell to the whale - a species of deep significance in local Indigenous lore. (AFP)