An air traffic controller detected smoke coming out of the right engine of the Boeing-777 at 7:41 am (Tuesday 2241 GMT) as it landed at Narita airport near Tokyo, transport ministry spokesman Fumio Shishiro said.
The plane, which had arrived from Ho Chi Minh City, taxied to the terminal and let passengers disembark, after which plumes of white smoke billowed out of the engine, television footage showed.
Around an hour after the passengers had exited, a fire broke out but it was doused by firefighters who were on standby, he said.
"There was a slight smell as if the engine was burning," a male passenger told NHK television.
Police were investigating the cause of the fire, Shishiro said.
None of the 264 passengers and 13 crew were injured, the official said. Airport officials closed part of the runway but reopened it later, he said.
Vietnam Airlines said in a statement that the crew of flight VN 950, while taxiing at Narita, "discovered the alarm signal showed that the temperature had exceeded the limit, and there was smoke at the right engine number two."
"The crew performed technical steps following procedures," the Vietnamese-language statement said.
"When the alarm signal on the plane went back to normal, the pilot continued to taxi the plane to the pier and the passengers went to the terminal normally."
Narita airport used a firefighting truck to tackle smoke still coming from the engine as the plane sat at the terminal, the statement added.
The airline and airport authorities are investigating the cause of the incident, Vietnam Airlines said.