The bizarre demonstration was staged at a royal residence in Riyadh and was sparked by the signing of a decree halting state payments to over their utilities bills.
The princes were also demanding compensation for the 2016 state execution of a cousin who was convicted of murder.
Saudi Attorney General Sheikh Saud al-Mojeb said the princes were warned their demands were unlawful but they refused to leave and public peace and order was disrupted.
The princes were arrested and are being held at al-Hayer prison south of Riyadh pending trial.
Sheikh al-Mojeb said: “No one is above the law in Saudi Arabia. Everyone is equal and is treated the same as others.”
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Two months ago, authorities arrested dozens of royals, businessmen and senior government officials as a part of a corruption crackdown.
Those detained included the former head of the royal court Khaled al-Tuwaijri and Saudi media mogul Waleed al-Ibrahim.
The investigation is being overseen by Crown Prince Mohammed bin Salman who was appointed head of a new anti-corruption committee hours before the arrests began November 4.
The royal decree said the committee was needed “due to the propensity of some people for abuse, putting their personal interest above public interest, and stealing public funds” and will “trace and combat corruption at all levels”.
Saudi officials said decades of corruption and embezzlement had cost the kingdom tens of billions of pounds.