Flood control authorities warned south-central provinces that rivers were rising and they should prepare for flooding in the aftermath of Durian.
The storm was downgraded to a tropical depression and was heading west across the Gulf of Thailand on Wednesday.
Forecasters said it would spare Malaysia but strong winds were expected to hit parts of the country.
The storm struck the coast on Monday night and Tuesday with 120kph winds.
Nguyen Sinh Hung, the deputy prime minister, called on officials to "expand their efforts to continue to rescue and find missing people" and "mobilise military police and the youth union to help".
Vietnam's national flood and storm control centre said in a report on Wednesday that Typhoon Durian killed at least 48 people in four south-central provinces of Binh Thuan, Ba Ria Vung Tau, Ben Tre and Vinh Long.
It said 49 people were missing and that 433 were injured.
Durian, the ninth storm to hit Vietnam this year, damaged or destroyed 120,899 houses and sank 696 fishing vessels, the report said.
