Flight MH370 vanished at 18:40 GMT Friday (02:40 local time Saturday) after leaving Kuala Lumpur for Beijing.
It had been expected to land in the Chinese capital at 22:30 GMT.
The aerial search has now been halted for the night but operations at sea continue. No wreckage has been reported by the airline.
Distraught relatives and loved ones of those aboard are being given assistance at the airports.
"We are doing everything in our power to locate the plane," Malaysian Transport Minister Hishammuddin Hussein told reporters in Kuala Lumpur.
The plane went off the radar south of Vietnam, according to a statement on the Vietnamese government website.
Its last known location was off the country's Ca Mau peninsula although the exact position was not clear, it said.
The Boeing B777-200 aircraft was carrying 227 passengers, including two children, and 12 crew members.
A Vietnamese navy official told the BBC the plane had gone missing within Malaysian maritime territory.