Flash floods and heavy rain also injured 27 others and damaged thousands of hectares of rice paddies, the Central Steering Committee on Natural Disaster Prevention and Control said in a report.
Among the dead were two villagers killed when landslides collapsed their tents in a forest.
The missing include two workers who were swept away when a hydroelectric dam burst in central Vietnam earlier in the week.
Flash floods have also caused nearly 80 homes to collapse, with another 2,000 houses submerged and more than 1,200 roofs were torn off of others.
Heavy rains have left nearly 12,000 hectares of rice paddies submerged.
In other damages, thousands of cattle and poultry have been killed, six fishing vessels demolished, 19 bridges swept away, with untold numbers of electric poles and transformers damaged.
Tropical storm Rai brought strong winds of up to 80 kilometres per hour when it swept through central Vietnam early on September 13. It weakened into a tropical depression and has now moved into southern Laos.