Australian officials said the objects were spotted by satellite in one of the remotest parts of the globe, around 2,500 km (1,500 miles) southwest of Perth in the vast oceans between Australia, southern Africa and Antarctica.
The larger of the objects measured up to 24 metres (79 ft), long and appeared to be floating on water several thousand metres deep, they said.
"It's credible enough to divert the research to this area on the basis it provides a promising lead to what might be wreckage from the debris field," Royal Australian Air Force Air Commodore John McGarry told a news conference in Canberra.
No confirmed wreckage from Malaysia Airlines Flight MH370 has been found since it vanished from air traffic control screens off Malaysia's east coast early on March 8, less than an hour after taking off from Kuala Lumpur for Beijing.
"I can confirm we have a new lead," Malaysian Transport Minister Hishammuddin Hussein told reporters in Kuala Lumpur, where the investigation into the missing airliner is based.
Another official in Malaysia said investigators were "hopeful but cautious" about the Australian discovery.
The fate of Flight MH370 has been baffling aviation experts for nearly two weeks.
Investigators believe that someone with detailed knowledge of both the Boeing 777-200ER and commercial aviation navigation switched off the plane's communications systems before diverting it thousands of miles off its scheduled course.
Exhaustive background checks of the passengers and crew aboard have not yielded anything that might explain why.
An Australian air force AP-3C Orion plane was already at the scene, and more aircraft were on the way, John Young, general manager of the emergency response division of Australian Maritime Safety Authority (AMSA), told the news conference in Canberra.
A merchant ship diverted for the task was due to arrive in a few hours, he said. A Royal Australian Navy ship equipped to recover any objects was also en route, but was still "some days away".
China, whose citizens made up about two-thirds of the passengers on board the flight, said it was also sending ships to the area of the sighting, but it was not clear how long it would take for the vessels to reach the scene.
The huge potential breakthrough in an investigation that had appeared to be running out of leads was revealed by Australian Prime Minister Tony Abbott, who told parliament the objects had been located with satellite imagery.
"New and credible information has come to light in relation to the search for Malaysia Airlines Flight MH370 in the southern Indian Ocean," Abbott said.
He added that he had already spoken with his Malaysian counterpart, Najib Razak, and cautioned that the objects had yet to be identified.
"The task of locating these objects will be extremely difficult and it may turn out they are not related to the search for MH370," Abbott said.
Young, the Australian official, said it could be some days before authorities have anything to report and added that poor visibility reported in the area could hamper the search.
"It's probably the best lead we have right now but we have to get there, find them, see them, assess them, to know whether it's really meaningful or not," he said.
The dimensions given are consistent with at least one of the objects possibly being the major part of a 777-200ER wing, which is around 27 metres (89 feet) long, though Australian officials cautioned the first images were indistinct.
The relatively large size of the objects would also suggest that, if they do come from the missing aircraft, it was intact when it went into the water.
FBI HELPING PROBE
Investigators piecing together patchy data from military radar and satellites believe that, minutes after its identifying transponder was switched off as it crossed the Gulf of Thailand, the plane turned sharply west, re-crossing the Malay Peninsula and following an established commercial route towards India.
What happened next is unclear, but faint electronic "pings" picked up by one commercial satellite suggest the aircraft flew on for at least six hours. That would be consistent with the plane ending up in the southern Indian Ocean.
The methodical shutdown of the communications systems, together with the fact that the plane appeared to be following a planned course after turning back, has focused particular attention on the pilot and co-pilot.
The FBI is helping Malaysian authorities analyse data from a flight simulator belonging to the captain of the missing plane, after initial examination showed some data logs had been deleted early last month.
A Malaysian official with knowledge of the investigations into the pilots said three simulator games that 53-year-old pilot, Zaharie Ahmad Shah, had played were being looked at.
"We are following up on the data logs being erased," the source said. "These could be logs of the games that were erased to free up memory, so it may not lead us to anything. He played a lot of games, going into hundreds and thousands of hours."
An unprecedented multinational search for the plane has focused on two vast search corridors: one arcing north overland from Laos towards the Caspian Sea, the other curving south across the Indian Ocean from west of Indonesia's Sumatra island to west of Australia.
Australia is leading the search in the southern part of the southern corridor, with assistance from the U.S. Navy.
The depth of the water where the possible debris has been sighted would likely make recovering the "black box" voice and data recorders that may finally unlock the mystery of what happened aboard Flight MH370 extremely challenging.
University of Western Australia Professor of Oceanography Charitha Pattiaratchi said that, based on currents in the area, if the debris is from the plane it probably would have gone into the water around 300-400 km (180-250 miles) to the west.
The search area covered an ocean ridge known as Naturalist Plateau, a large sea shelf about 3,500 metres (9,800 feet) deep, Pattiaratchi said. The plateau is about 250 km (150 miles) wide by 400 km (250 miles) long, and the area around it is close to 5,000 metres (16,400 feet) deep.
"Whichever way you go, it's deep," he said.