Vorayuth "Boss" Yoovidhya left Thailand for Singapore on April 25, two days before he had been ordered to report to prosecutors to be formally charged in court, police said.
He faces charges of speeding, hit-and-run and reckless driving causing death over an incident in 2012 when he allegedly crashed his Ferrari into a policeman on a motorcycle in Bangkok and fled the scene, dragging the officer's body for several dozen meters with his car as he did so.
It was the eighth time he has missed a summons since legal proceedings against him began in 2016.
The case is being closely watched in Thailand where it has fuelled complaints that the justice system favours the rich and famous, allowing them to break the law with impunity.
Police said Vorayuth had travelled to Singapore on his private jet and stayed there for two days.
"Vorayuth left Singapore on April 27. The private jet he arrived in is still there," senior police official Apichat Suriboonya, who heads Thailand's Interpol bureau, told Reuters.
"We have no further details."
Mr Apichat said his team was working with Singapore police to try to determine where Mr Vorayuth had gone. Singapore police confirmed he had left the city state and said they would do what they could to help their Thai colleagues.
A Thai court issued an arrest warrant for Mr Vorayuth last Friday and police said they had asked the Foreign Ministry to revoke his passport. The ministry said it would do so as quickly as possible.
"Having his passport revoked will pressure Vorayuth to travel back to Thailand, as no country would allow him to enter without it," another senior police official, Sarawut Detsri, told Reuters.
Mr Vorayuth is a grandson of the late Chaleo Yoovidhya, creator of the Kratin Daeng, or red bull, energy drink.
Mr Chaleo, 88, was listed as the third richest person in Thailand at the time of his death in 2012, with an estimated net worth of US$5 billion, according to Forbes magazine.
Mr Vorayuth has spent much of the past five years abroad, including in London, where his family owns a home, and Singapore, according to social media posts.
He has previously cited work commitments abroad as a reason for not showing up in court.
(Reporting by Patpicha Tanakasempipat and Panarat Thepgumpanat in BANGKOK; Additional reporting by Fathin Ungku in SINGAPORE; Editing by Amy Sawitta Lefevre and Robert Birsel)