The accident occurred at about 4.15am at kilometre marker 45 near Ban Khlong Khan in tambon Tham Niap.
Uthai Somkantha, 30, the bus driver, said the bus left Bangkok at 7pm last night with 29 passengers, heading for Phuket.
At Ban Khlong Khan, he lost control of the bus at a sharp curve because the road was wet and slippery, causing the vehicle to overturn and lie on one side.
Fifteen passengers were injured and admitted to Khirirat Nikhom Hospital.
Seven of them were later transferred to Surat Thani Hospital and four to a hospital in Phuket, said police, while the other four were released.