Family and colleagues of Rybkin, who was a senior official in former President Boris Yeltsin's government, say he has disappeared, BBC reports.
Rybkin only gained approval as a candidate from the election officials Saturday, two days after he vanished, the report said.
Rybkin is a harsh critic of Putin, accusing him of ruling by fear. Putin expects to win with ease in the elections on March 14.
There are currently five candidates for the Russian presidency, and two others are seeking the approval of the electoral commission.
Rybkin is best known as a speaker of the Russian parliament and head of the national Security Council during the Yeltsin era. He has been an advocate of talks between the Kremlin and Chechen rebels on ending that dispute. Putin is opposed to any negotiation.