Highway Police Senior Sgt-Major Chaiwichit Saensub said he signalled the suspected vehicle to stop at a Sing Buri border checkpoint but the driver drove past him at high speed.
Chaiwichit soon followed the grey Toyota Vigo pickup into Ayutthaya, where it overturned near Khlong Ban Na Village in Maharat district. Several passengers were thrown overboard in the crash.
Three male passengers were killed by the impact, while 15 others were injured, 11 of whom were taken to Maharat Hospital and four to Ang Thong Hospital.
All the passengers are Myanmar nationals.
The truck was severely damaged but there was no sign of the driver. Police speculated he might have escaped after the accident.
One of the injured migrants reportedly said the truck belonged to a gang that had been smuggling migrant workers from Myanmar into Thailand.
Police are collecting evidence to track down the driver and the gang behind the operation.