The volcano erupted in the eastern part of Java late Thursday -- at least two days after it began spewing ash and smoke into the air, CNN reported.
Indonesia's disaster management agency said three people were killed; two from smoke inhalation and the third by a collapsing wall.
More than 75,000 people had been evacuated from their homes, CNN said.
The BBC reported the city of Kediri was covered with gray and white ash, making it dangerous for pedestrians and people in vehicles.
Spreading volcanic ash forced the cancellation of flights and closure of airports in East and Central Java. The Indonesia Transport Ministry said the closed airports included the Juanda Airport in Surabaya, provincial capital of East Java, Adi Sucipto in Yogyakarta and Adi Sumarmo in Solo, China's Xinhua News Agency reported. The ministry warned aircraft to avoid flying through the ash, which could endanger their engines.
The 5,679-foot-high volcano, which began erupting for the first time since 2007, was sending ash 55,700 feet into the air, Khairul Huda, head of the Mount Kelud observation post, told Xinhua.
A Kediri police official said personnel had been deployed at various evacuation centers, the Antara news agency said. The military deployed around 1,000 personnel to assist in the relief and rescue effort.
The Jakarta Globe reported quoted experts as saying the eruption followed a seismic earthquake.
Mount Kelud erupted less than 2 hours after authorities had raised the volcanic alert level to its highest point on a four-point scale.
Some people who are used to volcanic activity had begun to leave the area hours before the eruption, authorities said.
CNN quoted National Disaster Mitigation Agency spokesman Sutopo Purwo Nugroho as saying lightning was seen striking the crater as it spewed debris.
The volcanology agency warned there could be smaller eruptions.
Earlier this month, an eruption at Mount Sinabung on the island of Sumatra killed at least 14 people.