It is expected the journey will take more than two days to travel the thousands of miles through China to Vietnam.
Mr Kim is accompanied by his sister Kim Yo Jong and Kim Yong Chol, who has been a key negotiator in talks with the US.
Before departing, the North Korean leader inspected a guard of honour at the Pyongyang station.
The much anticipated Trump-Kim meeting is due to take place on Wednesday and Thursday in Hanoi.
It follows their historic summit last June in Singapore which ended without substantive agreements on the North's nuclear disarmament.
It also triggered a months-long stalemate in negotiations as Washington and Pyongyang struggled with the sequencing of North Korea's nuclear disarmament and the removal of US-led sanctions against the North.
Vietnam's foreign ministry announced on Saturday that Mr Kim would pay an official goodwill visit to the country "in the coming days" in response to an invitation by president Nguyen Phu Trong, who is also the general secretary of Vietnam's ruling Communist Party.
In his upcoming meeting with Mr Trump, experts say Kim will seek a US commitment for improved bilateral relations and partial sanctions relief while trying to minimise any concessions on his nuclear facilities and weapons.
While Kim wants to leverage his nuclear and missile program for economic and security benefits, there continue to be doubts on whether he is ready to fully deal away an arsenal that he may see as his strongest guarantee of survival.
Last year, North Korea suspended its nuclear and long-range missile tests and unilaterally dismantled its nuclear testing ground and parts of a rocket launch facility without the presence of outside experts, but none of those steps were seen as meaningful cutbacks to the North's weapons capability.
While North Korea has repeatedly demanded that the United States take corresponding measures, including sanctions relief, Washington has called for more concrete steps from Pyongyang toward denuclearisation.