Feinstein claimed that the agency secretly searched off-site computers used by committee staffers at a secure CIA location.
Feinstein's source of information is CIA Director John Brennan, who she says briefed her in January about what Brennan called a "search" of the computers her staffers were working on.
"Based on what Director Brennan has informed us, I have grave concerns that the CIA's search may well have violated the separation-of-powers principles embodied in the United States Constitution, including the speech and debate clause," Feinstein said on the Senate floor.
Feinstein said that she had been working with Brennan and the CIA to resolve the situation, but had little success.
"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."
But in response to Feinstein's speech, Brennan denied the allegations, saying "nothing could be further from the truth."
"That's just beyond the scope of reason," Brennan said during an event at the Council on Foreign Relations.
Meanwhile, Sen. Patrick Leahy, D-Vt., called Feinstein's speech "one of the best speeches I'd ever heard" in his 40 years serving in the Senate.
"I think that if we're going to have real oversight in the Senate you have to have people doing what Sen. Feinstein has," he told reporters afterwards.