The area between Thua Thien-Hue and Phu Yen provinces, which are 530 kilometers apart, is home to many popular tourists destinations, and they have been hit by winds of up to 135 kph.
Gia Lai in the Central Highlands, 250 km away, is also being battered by heavy rains and strong winds.
Minister of Agriculture and Rural Development Nguyen Xuan Cuong said many parts of the central region have been experiencing power outages.
Hundreds of roofs have been blown away and some public works in Quang Ngai Province have been badly damaged.
Two fishing boats sank in Binh Dinh Province on Tuesday night while trying to seek shelter, and 26 fishermen on board are missing.
There have been no other reports of human casualties so far.
The region has been hit by torrential downpours since Tuesday night.
In the ancient town of Hoi An in Quang Nam Province, many streets are flooded.
The National Center for Hydro-Meteorological Forecasting, which described Molave as the most powerful storm to hit the country in the last 20 years, has warned it is especially dangerous because of its swiftness, intensity and size.
In the next 12 hours the storm is expected to move west at a speed of 25 kph and weaken into a tropical depression.
By around 10 p.m. on Wednesday it will move to southern Laos with winds of 60 kph.
Before entering the East Sea, Storm Molave had wreaked havoc in the Philippines, killing at least three people and leaving dozens missing, the country’s National Disaster Risk Reduction and Management Council said on Tuesday.
Natural disasters, mostly floods and landslides triggered by storms and heavy rains, killed 132 people and injured 207 in Vietnam last year.
- Storm Linfa to hit flooded central Vietnam
- Storm Linfa to compound woes for flooded central Vietnam
- Storm Molave hits the Central Coast
- 17 dead, 13 missing in central Vietnam floods
- Central Vietnam braces for torrential downpours
- Central region battens down the hatches
- Central Vietnam will experience torrential downpours as storm Saudel weakens into tropical depression
- Storm Molave gains strength, threatening central region
- Typhoon Molave nears mainland of central Vietnam