According to the Bangkok Post, the hit-and-run occurred in Bangkok early on Monday morning and Vorayuth Yoovidha, 27, was later detained by police.
He now faces charges of causing death by dangerous driving and failing to stop and inform the authorities, which could lead to a 10-year prison sentence and a fine.
Police searched the compound of late Red Bull magnate Chaelo Yoovidhya (who died earlier this year) and found a badly damaged Ferrari.
Vorayuth Yoovidha reportedly struck the police officer who was riding a motorcycle, but the Associated Press (AP) claimed the officer had cut across the car’s path.
The case has stoked controversy in Thailand since the nation’s highest ranking policeman has personally taken charge of it, after a more junior officer initially tried to cover up the alleged crime.
Forbes ranked the Yoovidhya family as Thailand’s fourth richest in 2012, with a net worth of $5.4bn that includes shares in Red Bull and a large property portfolio.