In a case closely watched by the Thai public, police said the court issued the warrant for Worayuth Yoovidhya after hours of deliberation by the bench.
Worayuth was allegedly behind the wheel when his Ferrari ploughed into a policeman in the early hours of the morning, dragging the body for several hundred metres before fleeing the scene.
"The arrest warrant has been issued," Col Kachornpong Jiitparkpoom, the superintendent of Thonglor police station, told AFP on Friday afternoon.
It is the first warrant against Worayuth, who has spent years ducking hearings on charges linked to the death which took place in Bangkok's wealthiest neighbourhood.
He was 27 at the time of the crash and has freely dipped in and out of Thailand over the past five years, with frequent appearances on Bangkok's rich kid party scene.
Several of the charges against him have expired during that time. But the most serious offence – a possible 10-year sentence for reckless driving that resulted in death – is valid until 2027.
For many in Thailand, the case has become a byword for the special treatment enjoyed by elites in a justice system notoriously bent by cash and influence. Worayuth's family are the fourth richest in Thailand.
In a move that critics say was long overdue, prosecutors called on police to request the warrant after Worayuth dodged yet another court hearing Thursday (read more here).
Thailand's top cop, Gen Chaktip Chaijinda, said his force is exploring applying for the extradition of Worayuth, who is a frequent overseas traveller.
"Initially I learned that he is hiding in England where we have an extradition treaty," the National Police Chief told reporters.
Worayuth's lawyer has previously said his client was unable to come to Bangkok because of business in the UK.
Worayuth's grandfather Chaleo Yoovidhya co-founded the Red Bull brand with Austrian Dietrich Mateschitz in the 1980s in the kingdom's most celebrated rags-to-riches tale.
Chaleo died in March 2012 aged 89, leaving his eleven surviving relatives with a collective wealth of $22 billion, according to Bloomberg.