At least four fishermen in the port city of Balikpapan were killed over the weekend when the fuel ignited.
Hundreds of people have reported health issues since Saturday's spill.
It is not clear what caused the oil spill. As it continues to spread, the risk of further fires is increasing, the authorities said on Tuesday.
The Balikpapan environmental agency has warned members of the local community to avoid any activities "that could spark fires".
The spill, which threatens to further contaminate the fishing waters along the coast, currently covers an area of 12 sq km (seven sq miles).
In addition to the four reported deaths, local health officials have said that hundreds of people in the area have experienced difficulty breathing, nausea and vomiting since the oil fires broke out.Image copyright Getty Images Image caption
Issuing a state of emergency allows for the release of government funds to aid local authorities in their efforts to contain the spill and for any subsequent clean-up operations.
Balikpapan, which is in East Kalimantan province, is home to a large oil refinery belonging to the state-owned company Pertamina. As investigations continue into how the oil escaped into the sea, Pertamina says its underwater pipeline has not leaked.
A general manager at the refinery told the Jakarta Post on Saturday that the spill was marine fuel oil, not crude.
Fishermen in Balikpapan say they will take part in a protest on Wednesday to hold the Indonesian government and Pertamina to account for the spill.
Pertamina has denied responsibility for the disaster.