A statement said King Bhumibol Adulyadej had accepted Princess Srirasmi's written request.
Crown Prince Vajiralongkorn had asked the government to strip his wife's family of their royally bestowed name.
Seven of her relatives had been arrested in a purge of officials allegedly involved in corruption.
The palace statement, which appeared in the Royal Gazette, read: "Princess Srirasmi, wife of Crown Prince Maha Vajiralongkorn... has written to respectfully resign from her status in the royal family and permission has been granted by His Majesty the King."
Srirasmi is the crown prince's third wife, and the pair married in 2001. They have a son.
He was already known to be estranged from the princess, although they continued to attend official functions together.