Prince Nayef, who was also deputy prime minister and interior minister, had left the country for a holiday and medical tests late last month.
On 3 June, the deputy interior minister said the prince, who was 77 or 78, was in good health and would return "soon".
He was named crown prince in October 2011 after the death of the previous crown prince, Sultan bin Abdul Aziz.
The succession in Saudi Arabia still passes among the sons of former King Abdul Aziz ibn Saud, who established the modern kingdom during his reign from 1932 to 1953.
Next in line is expected to be Crown Prince Nayef's 76-year-old brother, Prince Salman, who was appointed defence minister in November after spending five decades as governor of Riyadh.
King Abdullah, who is 89 years old, had a back operation last year.
A statement from the king published by the official SPA news agency, said Prince Nayef had died on Saturday "outside the kingdom" and would be buried Sunday after prayers in Mecca. It gave no more details.
Unconfirmed reports said Prince Nayef had been receiving medical treatment since May at a hospital in the Swiss city of Geneva.
