Kim left the North Korean capital of Pyongyang at around 5 p.m. (0800 GMT) in an armored train, TASS said, citing a North Korean diplomatic source.
Vietnam's foreign ministry announced earlier on Saturday that Kim would make an official visit to Vietnam in "coming days" at the invitation of Nguyen Phu Trong, the president and general secretary of the Southeast Asian nation's ruling Communist Party.
The summit with Trump is scheduled for Feb. 27-28.