The threat comes after years of public anger over the lack of progress in a case that critics say highlights the impunity enjoyed by Thailand's wealthy and well-connected.
Worayuth Yoovidhya, whose nickname is "Boss", was 27 when he allegedly smashed his Ferrari into a police officer in the early hours of the morning, dragging the body for several hundred metres before fleeing the scene of the crash.
The scion, whose billionaire father is Thailand's fourth-richest man, has never showed up for a formal indictment, allowing some of the charges against him to expire.
After Worayuth missed the latest summons Thursday, prosecutors promised to request an arrest warrant from the Thai courts, a step which until now has never been taken despite his previous no-shows.
"If the suspect doesn't show up by 4pm today, tomorrow we will send a letter to Thonglor police station to ask the court for an arrest warrant immediately," Prayut Bejraguna, a spokesman for the Attorney-General's office, told reporters.
Prosecutors said they would also explore extraditing Worayuth, who has paraded his flashy lifestyle on social media over the years with frequent trips overseas.
His lawyer has previously said Worayuth was on business in the UK and unable to return to Bangkok.
"If our (extradition) request fails we can ask UK police to renew the case while we support them with details," said Amnat Chotchai, the head of the Attorney-General's foreign division.
Prosecutors faced a barrage of press questions about why the case had dragged on for so long. They denied Worayuth's family wealth had an impact.
"This has nothing to do with rich or poor," Attorney-General spokesman Prayut said. "We will provide justice for everyone involved."
A trail of debris from the accident led police to the Bangkok mansion of the princeling's super-rich clan, who own half of the Red Bull energy drink empire.
Thonglor police station, which covers one of Bangkok's most exclusive districts, initially accepted the family's claim that the housekeeper was driving the car.
But the story fell apart and Worayuth was eventually hit with a string of charges – including causing death by reckless driving, which carries a maximum 10 year jail term.
That charge will not expire until 2027.
Worayuth's grandfather Chaleo Yoovidhya co-founded the Red Bull brand with Austrian Dietrich Mateschitz in the 1980s.
Chaleo died in March 2012 aged 89, leaving his eleven surviving relatives with a collective wealth of $22 billion, according to Bloomberg.
The Red Bull brand has not made any recent public remarks on the affair, even though Worayuth has been seen attending some of their racing events since 2012.
"We do not have any comments on this topic," a company spokesman told AFP on Thursday.