The man, who is reported by Aftonbladet to be from western Sweden, died on Wednesday after having had dinner with his girlfriend.
“The cause of death remains unclear,” said Kent Öberg at the Swedish foreign ministry to the TT news agency.
His body is reported to be still in Indonesia.
The death comes just a year after 21-year-old Rasmuss Lindholm from Stockholm died after drinking the local “arrak” moonshine.
Gili Trawangan is one of three droplets of palm-fringed sand just off the coast of Lombok a neighbouring island to the major tourist destination of Bali.
The island is a popular weekend retreat for expats and tourists alike from Bali. The island is the liveliest and most developed of the three Gilis and is known for its club and party scene.
While the islands are predominantly Muslim, alcohol is widely available but is heavily taxed and thus the local moonshine is a popular and cheap alternative for mixing drinks.
The Swedish foreign ministry has issued a warning over the locally-distilled spirit following the death of Rasmuss Lindholm in June 2011.
Lindholm’s relatives have also urged the popular backpacker guidebook publisher Lonely Planet to carry a warning against the potentially fatal local liquor.