The Vatican made the announcement on Friday.
So far, no candidate stands out as a clear successor to the outgone 85-year-old pontiff, who blamed his failing health for his inability to continue in office. He becomes the first to resign in about 600 years.
Under the rules of the secret ballot or conclave, cardinals would vote until one achieves a two-thirds majority to emerge.
Agency sources quoted Vatican press office as saying that the vote would be preceded by a mass on Tuesday morning, with the first ballot due in the afternoon.
Vatican staff have been preparing the Sistine Chapel, where the conclave is expected to take place, installing the two stoves that would produce white smoke from burnt ballot papers when a new pope is elected.
The last election in 2005 took three days, and correspondents say the number of meetings this time is being seen as a reflection of the many challenges facing the Church.
There are also tensions between traditionalists and reformers over issues, including priestly celibacy, gay rights and the role of women.