"I can't say at this time how many passengers have been affected," said Farid Indra Nugraha, a spokesman for airport operator Angkasa Pura 1.
National flag carrier Garuda Indonesia cancelled all its flights to and from the four airports, it said on its official Twitter account, The Hindu reported.
"Bali is our second largest hub and this will also affect our international connecting flights," said Ikhsan Rosan, a spokesman for the airline.
Mount Raung in East Java has been erupting for nearly a week, forcing the cancellation of a number of flights to and from Australia.