Police said the bus hit the sign and fell into a ditch in the middle of the road in Tambon Tha Yang of Phetchaburi's Tha Yang district.
Rescuers took about half an hour to free the passengers trapped inside.
The injured were taken to the Phetchaburi Hospital.
The driver, Ekkalak Deesud, 36, admitted that he dozed off. He was detained to face a charge of reckless driving causing injuries.