Flight QZ8501 went missing at 07:24 (23:24 GMT), AirAsia tweeted.
The plane, an Airbus A320-200, disappeared midway into the flight of more than two hours and no distress call was issued.
Indonesian military planes and aircraft from Singapore are searching an area of the Java Sea.
The flight left the Indonesian city of Surabaya in eastern Java at 05:20 local time (22:20 GMT) and was due to arrive in Singapore at 08:30 (00:30 GMT).
The missing jet had requested a "deviation" from the flight path due to bad weather, AirAsia said.
Indonesia's transport ministry said the pilot had asked permission to climb to 38,000 ft (11,000m) to avoid thick cloud.
AirAsia, a budget airline which owns 49% of AirAsia Indonesia, is based in Malaysia and has never lost a plane.
However, 2014 has been a difficult year for aviation in Asia: Malaysia's national carrier Malaysia Airlines has suffered two losses - flights MH370 and MH17.
There were 155 passengers on board, the company said in a statement:
138 adults, 16 children and one infant
Two pilots and five cabin crew were also on board
Most on board were Indonesian
Six were from other countries: three South Koreans and one French, Malaysian and Singaporean.
The UK Foreign Office has confirmed that one Briton was on board the flight, and next of kin have been informed.
AirAsia has set up an emergency line for family or friends of those who may be on board. The number is +622 129 850 801.
Dozens of passengers' relatives have been gathering at Juanda airport in Surabaya and Singapore's Changi airport to hear news.
AirAsia's Chief Executive Tony Fernandes tweeted: "Thank you for all your thoughts and prayers. We must stay strong."
AirAsia Indonesia operates domestic flights round the Indonesian archipelago as well as international services to Malaysia, Singapore, Australia and Thailand.
AirAsia Indonesia was banned from flying to the European Union in 2007 due to safety concerns but this was lifted in July 2010.
Captain Desmond Ross, a former pilot, says the plane vanished in an area "well covered by radar"
The latest incident caps a tragic year for Malaysian aviation with the disappearance of one Malaysia Airlines plane and the downing of another.
Flight MH370 disappeared on a flight from Kuala Lumpur to Beijing in March with 239 passengers and crew. The wreckage, thought to be in southern Indian Ocean, has still not been located.
MH17 was shot down over Ukraine in July, killing all 298 on board.
Anxious family members have been arriving at the airport in Surabaya