The princes were protesting a recent royal order that “halted payments by the state to members of the royal family to cover their electricity and water utility bills,” Sheikh Saud Al Mojeb said in a statement.
They also want compensation for the 2016 state execution of a cousin who was convicted of murder, the statement said.
Authorities had told the princes their demands were unlawful, but they refused to leave and public peace and order was disrupted, the attorney general said.
The princes were being detained at Al-Hayer prison south of Riyadh, the capital, pending trial.
“No one is above the law in Saudi Arabia. Everyone is equal and is treated the same as others,” the statement said.
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.