The woman, named as Acting Sub Lieutenant Fadeeya Munoh, suffered a head injury in the collision, and was also rushed to hospital.
Police did not confirm whether Fadeeya is a policewoman, or serves with a branch of the military or other organisation.
Lt Col Thanyapisit Muangchan of the Thalang Police Station said was informed of the accident, on Thepkrasattri Rd in Moo 5, Srisoonthorn, at about 6am.
Kusoldharm Foundation rescue workers and Srisoonthorn Municipality Rescue Unit also soon arrived at the scene.
Anek Amnuaychokchai, 73, who had suffered a gaping wound to his left leg, was still lying on the back of the songthaew. Fadeeya had suffered a head injury.
Rescue workers administered emergency first aid to both then rushed them to Thalang Hospital.
The songthaew driver, Sin Sittisak, 63, told police that Mr Anek was waiting for the songthaew by the side of the road.
He signalled for the songthaew to stop, so Mr Sin pulled over so he could get on board.
As Mr Anek was about to get into the songthaew he was struck by the Honda PCX motorcycle being ridden by Fadeeya. The motorbike was travelling at speed when it crashed into the songthaew, he said.
Police said they were continuing their investigation into the accident.