Prince Nayef (search) gave no details of their arrests, their identities or what they were charged with.
"We ... handed to America the Americans wanted in cases related to the United States. They were handed over and they are more than three," Nayef was quoted as saying by the Saudi Press Agency. He did not said when the transfer occurred.
Asked if the extradited Americans were wanted in terror cases, Nayef replied: "So it was said."
Nayef also said the kingdom arrested four armed men near the border with Iraq on Monday.
"We think they are wanted (suspects) because they were fleeing" Saudi Arabia, he was quoted as saying.
Saudi Arabia cracked down on Islamic militants after suicide bombers struck expatriate housing compounds in the capital, Riyadh, on May 12.
About 200 people have been detained in the crackdown, and more than 10 people have been killed in shootouts with security forces.
Prince Nayef said those arrested near the Saudi town of Arar, close to the Iraqi border, might be wanted in the hunt for Islamic extremists.