Bangkok's top police official, Lt Gen Comronwit Toopgrajank, said that he took charge of the investigation after a lower-ranking policeman was said to have tried to cover up the crime by turning in a bogus suspect.
Lt Gen Comronwit led a team of officers to search the compound of late Red Bull founder Chaleo Yoovidhaya, one of Thailand's wealthiest men before he passed away this year, and confiscated a dark grey Ferrari with a dented front bumper as part of their investigation.
The victim, Sgt Maj Wichean Glanprasert, 47, was killed during a pre-dawn motorcycle patrol. Thai media reported that the car dragged the officer and his motorcycle for several dozen feet as it sped through the residential neighbourhood.
The police chief said he suspended the police officer who allegedly attempted to subvert the investigation.
He said: "A policeman is dead. I can't let this stand. If I let this case get away, I'd rather quit," he told reporters.
"I don't care how powerful they are. If I can't get the actual man in this case, I will resign."
Vorayuth, who is believed to be in his late 20s, belongs to the third generation of the Yoovidhaya family, which was ranked fourth richest in Thailand this year by Forbes magazine with a net worth of 5.4 billion US dollars (£3.4 billion).
Red Bull creator Chaleo passed away in his 80s in March, leaving his heirs a wide range of businesses, including shares in the globally popular energy drink brand, hospitals and property. The family also co-owns a company that is the sole authorised importer of Ferrari cars in Thailand.