Twenty-six American defendants - 25 CIA agents and a US air force colonel - are being tried in absentia in the case looking at the detention of Osama Mustafa Hussan, also known as Abu Omar.
Seven Italians, including Nicolo Pollari, the former head of Italian military intelligence, are also before the court.
Abu Omar, was seized from a Milan street on February 17, 2003, in an operation led by the CIA and Italian military intelligence.
He was sent to a high-security prison outside Cairo, where he was held for four years.
After his release in February 2007, he said he had been tortured and had to endure humiliating treatment throughout his detention, such as being forced to defecate on the floor of his cell.
Case 'not over'
Ignazio Francesco Caramazza, a lawyer for the Italian government, said the ruling marked a "full victory" for the state.
"I'm very satisfied. Frankly, I didn't expect so much," he told the ANSA news agency.
But Alessandro Pace, a lawyer for the prosecution, said the decision by the constitutional court does not mean that the case is doomed.
"The trial still holds, and only part of the evidence, and not all of the wiretap transcripts, are covered by the state secrecy laws," he said.
The prosecution had said that "facts [such as the kidnapping] which jeopardise the constitutional order cannot be covered by state secrecy laws".
But state secrecy could be invoked in the "higher goal of defending national security" and was therefore a "restraint on judicial power", Caramazza had argued before the court.
The court's next hearing is on Wednesday.