Tigerair has issued a statement saying that "conditions are not suitable for operations into and out of Denpasar Airport today due to volcanic activity from Mt Rinjani".
Perth Airport says it is monitoring the ash cloud with the help of the Bureau of Meteorology's Volcanic Ash Advisory Centre.
Travellers have been left stranded because the ash cloud - produced by eruptions by volcanos including Mt Rinjani - can interfere with jet engine turbine blades and choke intakes.
"Decisions about flights are made by individual airlines and operators. Safety is and always will be the highest priority," a statement reads.
The volcano has erupted several times recently, including November last year and last month.
The eruptions have caused confusion and delays for travellers - often extending for weeks at a time.