Tributes have been paid to an Italian surfer after she was stabbed in the chest by a swordfish and died off the western coast of Indonesia, the travel agency where she worked said this week.

Giulia Manfrini, 36, was surfing when she was struck by a fish with a long, pointed bill in the Mentawai islands off the coast of Sumatra island last week.

"She was surfing on the waters off Masokut Island. A swordfish suddenly jumped and struck her in the chest," Mentawai disaster mitigation agency's acting head Lahmudin Siregar told AFP on Tuesday.

"They brought her to the nearest health clinic but as soon as they arrived, she did not make it."

Lahmudin told state news agency Antara that the swordfish had caused a wound 2 inches deep.

The resort where she had been staying said she loved surfing in the region.

"She was hit in the chest by a needlefish and died almost immediately," Hidden Bay Resort Mentawais said in an Instagram statement on Monday.

"We do know, however, that she continued to do what she loved best and without suffering. May you follow your path of light and may you surf the eternal waves on the other side."

James Colston, the co-founder of Manfrini's travel agency AWAVE Travel, said in a statement Sunday that she "died doing what she loved, in a place that she loved" in what he called a "freak accident."

In a social media post, Colston said: "Even with the brave efforts of her partner, local resort staff and doctors, Giulia couldn't be saved."

The company's website says Manfrini was a former professional snowboarder who is the head of its surf resorts sales.

"Giulia was the lifeblood of this company and her infectious enthusiasm for surf, snow and life will be remembered by all that came in contact with her," Colston said.

Fabio Giulivi, the mayor of Manfrini's hometown Venaria Reale, said that surfing and opening a travel agency had been her "double dream," the BBC reported.

Last year, American professional surfer Mikala Jones died at age 44 after a surfing accident in the same region of Indonesia.

Previous research indicates that swordfish attacks are extremely rare, but in 2015, a man was killed in Hawaii when he was impaled by the bill of a swordfish.

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