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.
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," according to the release.
More than 200 people were questioned at one point, officials said then. One of the people who was questioned and released was son of the late King Abdullah, Prince Miteb. An undisclosed financial settlement was agreed upon. The government said at the time it expected to release more people as other settlements were reached.
Saudi officials estimate that corruption and embezzlement has cost the kingdom at least $100 billion over decades.
The crown prince has already introduced sweeping changes including subsidy cuts, new taxes and the lifting of a controversial ban on women driving. Also this week, King Salman announced new cost-of-living allowances for military personnel, government employees and students, the state-run Saudi Press Agency reported.
Government employees will receive a monthly cost-of-living allowance of 1,000 riyals ($266) for one year. Military personnel serving in the Saudi-led coalition fighting in Yemen will receive a payout of 5,000 riyals ($1,333).
The decree also increases the stipend for students by 10% for one year and increases retirement allowances, the SPA reported. from cnn