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.
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.