Rice's lawyer notified the senators chairing the hearing of her decision not to attend in a letter. Two other former Obama administration officials are scheduled to testify before a Senate Judiciary subcommittee on Monday.
The subcommittee is one of three congressional panels investigating Russia's role in the 2016 election.
Rice's refusal to testify is the latest twist in the congressional investigations into possible links between Russia and the Trump campaign and the ongoing debate over whether the probes are truly independent and bipartisan.
CNN first reported Rice's decision.
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Rice became a central part of the Russia investigation when President Donald Trump said she may have committed a crime when she asked intelligence analysts to disclose the name of a Trump associate mentioned in an intelligence report.
Rice has said she did nothing improper. But she has become a key former Obama administration official in a position to answer questions from lawmakers.
Rice's attorney, Kathryn Ruemmler, said Rice is supportive of the committee's investigation, but it is rare for Congress to ask for testimony from a former president's national security adviser.
But unlike invitations extended to Yates and Clapper, Rice was invited to testify solely by subcommittee Chairman Lindsey Graham, R-S.C, not jointly with the panel's top Democrat, Senator Sheldon Whitehouse of Rhode Island, Ruemmler said.
Ruemmler said in the letter that Whitehouse notified Rice in writing that he did not agree with Graham's invitation, which Ruemmler described as a "significant departure from the bipartisan invitations extended to other witnesses."
Yates' and Clapper's upcoming public testimony is much- anticipated, as they were both scheduled to speak before the House intelligence committee in March. But that hearing was cancelled, some Democrats believe, because the White House wanted to limit what Yates could say. The House intelligence committee has yet to reschedule the public hearing.
Yates is expected to give senators details about her Jan. 26 conversation with the White House counsel about Trump's first national security adviser, Michael Flynn.