Bill de Blasio said the relevant municipal agencies had backed the idea.
The bronze Fearless Girl statue was placed on 8 March to draw attention to gender inequality and the pay gap in the corporate world.
The statue - which has become an instant tourist draw - had been due to be removed on Sunday.
Appearing next to the 4ft-tall (1.21m) statue in Manhattan on Monday, Mr de Blazio said it "means so much to the people of New York".
