"The head of government summons voters to the polls," on November 9 for the "first round of presidential election," and on "December 20 for the second round, if there is one," said a statement from Prime Minister Christian Ntsay's office.
The dates had already been proposed by the Independent National Electoral Commission.
The vote comes at a tense time on the large Indian Ocean island amid questions around Rajoelina's dual nationality.
Rajoelina, who won the last vote in December 2018, in an election beset by fraud allegations, was born in Antsirabe, a town in central Madagascar, but was secretly naturalized in France in 2014.
Under local law if a person acquires foreign citizenship, he or she automatically loses the Madagascan nationality, and cannot stand for public office in any election.
But Rajoelina's TGV party is vigorously disputing the interpretation of the law saying his dual citizenship does not stand in the way of his candidacy.
A former mayor of Antananarivo, the 49-year-old Rajoelina, first came to power in 2009, ousting Marc Ravalomanana with the backing of the military.
He returned to the presidency in 2019, after beating archrival Ravalomanana in the 2018 two-round election.
The opposition and rights groups accuse his government of stifling dissent in one of the poorest nations in the world.