The department said the affected provinces would be Chumphon, Surat Thani, Nakhon Si Thammarat, Phatthalung, Songkhla, Pattani, Yala, Narathiwat, Ranong, Phang Nga, Phuket, Krabi, Trang and Satun.
The rains and strong winds would be caused by the influence of an active low pressure cell over the lower South.
In the same warning issued at 5am on Saturday, the department said Typhoon Damrey was due 200km east of Ho Chi Minh City in Vietnam at a latitude of 12.7 degrees North and 110.6 degrees East longitude.
With sustained winds of 120km per hour, it is moving west at speeds of 20kph to the coast of lower Vietnam by Saturday. The storm would decline before covering Cambodia, the department added.
The warning said 2-3 metres high waves were likely in the Gulf and the Andaman Sea.