"I'm going for it with the aim of winning," Buzyn told French news agency AFP.
A ruling party source confirmed that she was quitting the government to launch her campaign and would be replaced in the coming hours.
Griveaux, a close ally of President Emmanuel Macron, pulled out of the race on Friday over a video posted online which showed a man masturbating, along with racy text messages sent to a woman.
His departure left Macron's Republic on the Move (LREM) party scrambling to find a replacement candidate for Paris mayor, just a month before the vote.
A haemotologist who entered politics after Macron's election 2017 Buzyn is seen as one of the stronger performers in government.
She faces a tough challenge to close the gap with incumbent Socialist Mayor Anne Hidalgo, who is leading in the polls.
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