The California Democrat said the CIA had searched -- without her knowledge or consent -- a stand-alone computer network established for the committee in its investigation of allegations of CIA abuse in a George W. Bush-era detention and interrogation program.
Feinstein, in a dramatic speech on the Senate floor Tuesday, said she has "grave concerns" that the search violated separation of powers principles guaranteed in the Constitution.
"It may have undermined the constitutional framework essential to effective congressional oversight of intelligence activities or any other government function," she said.
She said the CIA has refused to answer her questions on the matter.
"I have asked for an apology and a recognition that this CIA search of computers used by its oversight committee was inappropriate," she said. "I have received neither."
The chairwoman said CIA Inspector General David Buckley is investigating the agency's activities and has referred the matter to the Justice Department "given the possibility of a criminal violation by CIA personnel."
Feinstein also said the CIA falsely accused committee staff assigned to use the spy agency's computer network of wrongdoing. She said after Buckley began his investigation, the CIA's acting general council filed a crimes report with the Justice Department concerning the staffers' actions.
"Our staff involved in this matter have the appropriate clearances, handled this sensitive material according to established procedures and practice to protect classified information, and were provided access ... by the CIA itself," she said. "As a result, there is no legitimate reason to allege to the Justice Department that Senate staff may have committed a crime."
The chairwoman said she considers the move a blatant effort to intimidate her staff. "I am not taking it lightly," she said.
At issue is whether the CIA violated an agreement made with the Senate Intelligence Committee about monitoring the panel's use of CIA computers. The CIA provided the computers to congressional staffers in a secure room at its headquarters so the panel could review millions of pages of top-secret documents in the course of its investigation into the CIA's use of torture during the Bush administration.
Feinstein said she was reluctant to speak publicly about her concerns, but felt compelled to "set the record straight" to combat several misleading media reports on the matter in recent days.
CIA Director John Brennan has been strongly critical of the Senate claims.
"I am deeply dismayed that some members of the Senate have decided to make spurious allegations about CIA actions that are wholly unsupported by the facts," he said last week. "I am very confident that the appropriate authorities reviewing this matter will determine where wrongdoing, if any, occurred in either the executive branch or legislative branch.
"Until then, I would encourage others to refrain from outbursts that do a disservice to the important relationship that needs to be maintained between intelligence officials and congressional overseers."
The California Democrat has received strong support from colleagues and outside groups.
"Chairman Feinstein described a troubling pattern of interference and intimidation by the CIA that raises serious questions about possible violations of the Constitution and our criminal laws," said Senate Judiciary Committee Chairman Patrick Leahy, D-Vt.
"The members of the Senate must stand up in defense of this institution, the Constitution and the values upon which this nation was founded."
The American Civil Liberties Union also praised Feinstein for her "forceful, necessary and historic defense of the constitutional principle of separation of powers."
"After so many years of Congress being unable or unwilling to assert its authority over the CIA, Senator Feinstein today began to reclaim the authority of Congress as a check on the executive branch," said ACLU Senior Legislative Council Christopher Anders.
• An Associated Press report contributed to this article.