Indonesia AirAsia's Flight QZ8501, an Airbus A320-200, lost contact with air traffic control early on Sunday during bad weather on a flight from the Indonesian city of Surabaya to Singapore.
Indonesia's search and rescue agency confirmed the debris was from the plane. The agency's chief, Soelistyo, said "more than one" body had been recovered.
The plane has yet to be found and there was no word on the possibility of any survivors.
Pictures of floating bodies were broadcast on television and relatives of the missing gathered at a crisis centre in Surabaya wept with heads in their hands. Several people collapsed in grief and were helped away, a Reuters reporter said.
"You have to be strong," the mayor of Surabaya, Tri Rismaharini, said as she comforted relatives.
"They are not ours, they belong to God."
A navy spokesman said a plane door, oxygen tanks and one body had been recovered and taken away by helicopter for tests.
AirAsia chief Tony Fernandes, who has been in Indonesia since the plane went missing, said he was rushing back to Surabaya.
"Whatever we can do at AirAsia we will be doing," he said on Twitter.
About 30 ships and 21 aircraft from Indonesia, Australia, Malaysia, Singapore, South Korea and the United States had been involved in the search of up to 10,000 square nautical miles.
The plane, which did not issue a distress signal, disappeared after its pilot failed to get permission to fly higher to avoid bad weather because of heavy air traffic, officials said.
Flight QZ8501 was travelling at 32,000 feet (9,753 metres) and had asked to fly at 38,000 feet, officials said earlier.
Pilots and aviation experts said thunderstorms, and requests to gain altitude to avoid them, were not unusual in that area.
The Indonesian pilot was experienced and the plane last underwent maintenance in mid-November, the airline said.
Online discussion among pilots has centred on unconfirmed secondary radar data from Malaysia that suggested the aircraft was climbing at a speed of 353 knots, about 100 knots too slow, and that it might have stalled.
CLUES WHEN THINGS GO WRONG
The plane, whose engines were made by CFM International, co-owned by General Electric and Safran of France, lacked real-time engine diagnostics or monitoring, a GE spokesman said.
Such systems are mainly used on long-haul flights and can provide clues to airlines and investigators when things go wrong.
Three airline disasters involving Malaysian-affiliated carriers in less than a year have dented confidence in the country's aviation industry and spooked travellers across the region.
Malaysian Airlines Flight MH370 went missing on March 8 on a trip from Kuala Lumpur to Beijing with 239 passengers and crew on board and has not been found. On July 17, the same airline's Flight MH17 was shot down over Ukraine, killing all 298 people on board.
On board Flight QZ8501 were 155 Indonesians, three South Koreans, and one person each from Singapore, Malaysia and Britain. The co-pilot was French.
The Indonesian pilot was experienced and the plane last underwent maintenance in mid-November, the airline said. The aircraft had accumulated about 23,000 flight hours in some 13,600 flights, according to Airbus.
U.S. law enforcement and security officials said passenger and crew lists were being examined but nothing significant had turned up and the incident was regarded as an unexplained accident.
Indonesia AirAsia is 49 percent owned by Malaysia-based budget carrier AirAsia.
The AirAsia group, including affiliates in Thailand, the Philippines and India, had not suffered a crash since its Malaysian budget operations began in 2002.
India is waiting to know what went wrong with the missing plane and will investigate if AirAsia India is following all safety procedures, a senior Indian aviation ministry official told Reuters. AirAsia India, a joint venture of the Malaysian carrier, started flying this year and is expanding operations.
The plane's disappearance comes at a sensitive time for Indonesia's aviation authorities, as they strive to improve the country's safety reputation to match its status as one of the airline industry's fastest growing markets.
