The victims were caught in the flames on Thursday in the East Java national park, the ministry said on Friday. Two others suffered serious burns and are receiving medical treatment.
The ministry did not identify those killed. In a statement, it expressed "deep condolences" and paid tribute to the "courage and dedication" of officers, volunteers and residents working on the fire lines. The deaths, it said, were "a reminder that extinguishing forest and land fires is a high-risk operation", adding that safety "must be the main concern", including tracking fire spread and wind direction, keeping evacuation routes ready and assessing conditions before and during operations.
The fires have extended beyond Indonesia's borders, blanketing neighbouring countries in haze, Reuters reported. The islands of Sumatra and Borneo, close to Singapore and Malaysia, are the worst affected.
Satellite monitoring detected 799 high-confidence hotspots nationwide as of Thursday night, up 427 from the previous day, the ministry said. It cautioned that hotspots are not the same as fires, as one blaze can register as several.
Indonesian President Prabowo Subianto has approved accepting help from neighbouring countries, Foreign Minister Arrmanatha Nasir said, according to Reuters. Malaysia offered last month to send three helicopters, an aircraft and 52 personnel, but there has been no follow-up, Reuters reported. Singapore has also said it is ready to help.
The fires have caused respiratory problems for hundreds of thousands of people and forced school closures in Malaysia and East Timor, according to Reuters.