Church leaders will draw up a shortlist of three candidates; a full Church council, including lay people, will then choose one of them by Thursday.
It is the first election of a patriarch since the fall of the Soviet Union.
Alexiy II steered the Church through the transition from communist rule, when Russia was officially atheist.
Patriarch Alexiy II died on 5 December at the age of 79.
His successor will lead a growing Church of around 165 million followers, including nearly 70% of Russia's population.
Moral authority
Senior Church leaders will gather in Moscow's Cathedral of Christ the Saviour to begin deliberations about who should hold one of Christianity's most senior roles.
Analysts say the favourite to succeed Alexiy II is the current interim head of the Church, Metropolitan Kirill of Smolensk and Kaliningrad.
His main rival is said to be Metropolitan Kliment of Kaluga and Borovsk.
BBC religious affairs correspondent Christopher Landau says the new patriarch will have to decide how close the Church should be to the political establishment.
He must also consider relations with other churches, especially the strained relationship with the Roman Catholic Church, our correspondent says.
Alexiy II became the Primate of the Russian Orthodox Church in 1990, shortly before the collapse of the Soviet Union.
He was credited with helping restore the moral authority of the Church after decades of repression under communism.
He insisted on his Church's right to be the sole national church of Russia, bringing its scattered branches back under the control of the Moscow Patriarchate.
Alexiy II also moved the Church closer to political circles, often visiting the Kremlin and aligning himself with its foreign policy stances.+++++++++++++++++++++++++++++++++++++++++++++++++++
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(Source: BBC)