Upon arrest, they were sent to a notorious maximum-security facility south of Riyadh in contrast to dozens of other high-profile figures who were detained in a luxury hotel last year during an anti-corruption drive.
"They were arrested after they refused to leave the palace and were put in al-Ha'ir prison in preparation for their trial," the statement said.
The princes are expected to go on trial.
"The 11 individuals officially were arrested because they were complaining about the fact that they had asked for subsidies for water and electricity, and for some reason they were denied," said analyst Joseph Kechichian.
"Other reports say that in fact they were cousins of a prince who was executed in October 2016 and that they had come to ask for retribution," he added. "It's very conflicting at this point, we don't know exactly what is going on."
Saudi Arabia recently introduced a raft of economic reforms, including a value-added tax (VAT) and a halt to state payments of water and electricity bills for royal family members.
On Saturday, King Salman decreed a series of financial payouts to ease the cost of living. Each government employee will receive a monthly bonus of 1,000 riyals ($267) for the next year, while military personnel serving in Yemen will be paid a one-off fee of 5,000 riyals ($1,330).
Students will have their allowances increased by 10 percent for the next year, while retirees and social security recipients will get a monthly stipend of 500 riyals ($133).
The unemployment rate in Saudi Arabia surpassed 12 percent last year as the economy grappled with the fallout from low oil prices.
Crown Prince Mohammed bin Salman has been spearheading attempts to diversify the country's oil-dependent economy.
The VAT, implemented as of January 1, applies to a wide range of commodities, including food, clothes, entertainment, electronics, and telephone, water and electricity bills.
Its imposition is part of a region-wide measure agreed upon by the six Gulf Cooperation Council member states in Riyadh in 2016. The International Monetary Fund has estimated it will raise additional revenues of 1.5 to three percent of non-oil gross domestic product, depending on the country.
According to Saturday's decree, the Saudi government will absorb the cost of the tax for citizens purchasing private healthcare and education, and for first-time homebuyers of properties valued at up to 850,000 riyals ($226,660).