The Malaysia Airlines Boeing 777-200ER flight from Kuala Lumpur to Beijing had been missing for hours when Vietnam's Tuoi Tre news quoted Admiral Ngo Van Phat as saying he had asked boats from an island off south Vietnam to rush to the crash site.
If the report is confirmed, it would mark the U.S.-built airliner's deadliest crash since entering service 19 years ago.
Malaysia Airlines had yet to confirm that the aircraft had crashed.
Malaysia Airlines said earlier in the day that no distress signal had been given and cited early speculation that the plane may have landed in Nanming in southern China.
Malaysia Airlines Flight MH370, operating a Boeing 777-200ER aircraft, last had contact with air traffic controllers 120 nautical miles off the east coast of the Malaysian town of Kota Bharu, Malaysia Airlines chief executive Ahmad Jauhari Yahya said in a statement read to a news conference in Kuala Lumpur.
Malaysia and Vietnam were conducting a joint search and rescue, he said but gave no details. China has also sent two maritime rescue ships to the South China Sea to help in any rescue, state television said on one of its microblogs.
"We are extremely worried," Chinese Foreign Minister Wang Yi told reporters in Beijing before the Vietnamese report that the plane had crashed. "The news is very disturbing. We hope everyone on the plane is safe."
The Malaysia Airlines flight left Kuala Lumpur at 12.21 a.m. (11.21 a.m. ET Friday) but no trace had been found of the plane hours after it was due to land in the Chinese capital at 6.30 a.m. (5.30 p.m. ET Friday) the same day.
"We deeply regret that we have lost all contacts with flight MH370," Jauhari said.
Malaysia Airlines said people from 14 nationalities were among the 227 passengers, including at least 152 Chinese, 38 Malaysians, 12 Indonesians, six Australians and three Americans. It also said a Chinese infant and an American infant were on board.
If it is confirmed that the plane has crashed, the loss would mark the second fatal accident involving a Boeing 777 in less than a year and by far the worst since the jet entered service in 1995.
An Asiana Airlines Boeing 777-200ER crash-landed in San Francisco in July 2013, killing three passengers and injuring more than 180.
Boeing said it was aware of reports that the Malaysia Airlines plane was missing and was monitoring the situation but had no further comment. The flight was operating as a China Southern Airlines codeshare.
An official at the Civil Aviation Authority of Vietnam (CAAV) said the plane had failed to check in as scheduled at 1721 GMT while it was flying over the sea between Malaysia and Ho Chi Minh city.