The fires, which happen every year, are caused by slash-and-burn clearances on the islands of Sumatra and Borneo.
Paper and palm oil companies have been widely blamed for the practice.
Indonesia, which has repeatedly promised to stop the illegal fires, has sent hundreds of military personnel to try to put them out.
It has declared a state of emergency in Riau province, where the haze has been building for several weeks and pollution levels are hazardous to health.
In Malaysia, schools have been closed in the capital, Kuala Lumpur, and several other areas, while Singaporeans are being advised to avoid strenuous activity outdoors.
Smoke from huge forest fires in Indonesian has created a cloud of smog over the country, which has spread over neighbouring Malaysia and Singapore.