Jin Can’s body was found in a large, rainbow-coloured plastic bag in a canal in Bang Yai area on Saturday.
The third-year university student was tortured before she was killed three days before her body was found, police said.
Jin was kidnapped at 1.30am on Wednesday from a university, said Maj-General Noppasin Poolsawat, deputy chief of the bureau. He did not name the university.
CCTV footage from the area where Jin’s body was found showed one of the three suspects carrying the rainbow-coloured bag containing her body from a Mazda vehicle and dumping it in the canal.
Noppasin said the vehicle had been rented in Bangkok and returned to the rental agency by the suspects on Thursday.
The three suspects lived in Bang Yai sub-district but moved out of their residence at 3pm on Wednesday, he said.
Noppasin said they flew to Chengdu, China on Thursday.
"Investigators are gathering evidence to obtain arrest warrants for the three suspects," he said.
Officers at Bang Mae Nang Police Station said kidnappers had contacted Jin’s father via her WeChat account and demanded a ransom.
"The criminals demanded 500,000 yuan [about 2.5 million baht] from the victim's father," police said, citing information provided by a university lecturer.
"The father did not transfer the money because he was confused,” they said.
He has been frantically trying to contact his daughter since he received the ransom demand, they said.