The gate in Lao Cai Province has been closed since Monday afternoon until further notice, Vuong Trinh Quoc, head of the Lao Cai Economic Management Board, told VnExpress.
The border is linked by a bridge beneath which water has been rising in recent days due to the impact of the storm, which hit Vietnam Saturday evening.
When the rains stop and floodwaters recede, the two sides would evaluate the situation and choose a time for reopening, Quoc added.
On average, 500-600 trucks pass through the border gate every day. On Monday morning nearly 150 trucks passed through but 40 others were stuck on the Vietnamese side.
Hundreds of thousands of residents in Lao Cai and two other mountainous provinces, Cao Bang and Bac Kan, have been without power since Monday morning as the rain continued to pound down.
A bridge collapsed in northern Vietnam Monday morning, and 13 people are missing after being washed away by strong water.
Since then authorities have either stopped or limited traffic at many bridges across the north Vietnam, where heavy rainfall and flooding are expected for the next several days.