The landslides, which hit remote areas in the central province of Quang Nam a day earlier, killed 13 with 40 missing as rescue efforts were hampered by bad weather at the tail end of the storm, the government said.
"We can forecast the storm path or the amount of rain, but can't predict when landslides happen," deputy Prime Minister Trinh Dinh Dung said in a statement.
"The road is covered under deep mud and heavy rains are still lashing the area, but rescue work has to be carried out quickly," Dung said.
Since early October, Vietnam has been battered by storms, heavy rains and floods which have affected over a million people.
The government said Typhoon Molave had left millions of people without electricity and damaged 56,000 houses.
Twenty-six fishermen also remain missing after their boats sank when trying to return to shore on Tuesday with two navy vessels mobilised to find them.
Molave has weakened to a tropical depression after making landfall on Wednesday and is expected to reach Laos later on Thursday.
Heavy rain of up to 700 millimetres (27.5 inches) will continue in parts of central Vietnam until Saturday, Vietnam's weather agency said.