Swimming in beaches is also banned there.
Nguyen Duc Vu, head of the peninsula and tourist beaches management, said all routes to Son Tra have been blocked to ensure safety.
The central region has been battered by heavy rains for the last few days due to a low-pressure area in the East Sea, resulting in severe floods and landslides.
Many parts of Da Nang were flooded over the weekends, some with 1.5 m of water, throwing daily life into chaos.
Heavy downpours are expected to continue until Tuesday, with up to 400 mm of rains forecast.
Son Tra Peninsula, 10 km to the northeast of Da Nang, has luxury resorts and Buddhist spiritual sites such as the Linh Ung Pagoda near the sea.