Central Kalimantan police spokesman Edi Ciptianto said authorities were searching for a local man they believe sold liquor mixed with a homemade brew.
Three men were found dead on the ship, the Captain Kurbatskiy, on Thursday, Ciptianto said.
Four other crew members suffered from breathing problems, dizziness and vomiting after drinking the liquor and were rushed to a hospital, he said. One, a woman, died shortly after arriving at the hospital.
Ciptianto said experts were carrying out tests on the alcohol.
"We are still investigating the cause of their death and plan autopsies," he said
The Captain Kurbatskiy, with 24 crew, is in Indonesian waters to take on a cargo of iron ore from a port near the Borneo city of Banjarmasin.
Late last year, three Russian engineers who were in Indonesia to assemble fighter jets bought from Russia died at an air force base after suddenly falling ill. Autopsies found they had consumed rubbing alcohol, which is usually used as a disinfectant, local media reported.