The company says that surpasses first-day sales of the Xbox 360, the previous-generation model that went on sale eight years ago.
The new console was launched in 13 markets.
The software giant said Friday that it sold had out at most retailers and that it is working to replenish stocks. It added that in the first day of game play, fans killed over 60 million zombies in "Dead Rising 3" and drove more than 3.6 million miles on "Forza Motorsport 5."
The sales figure matches that of Sony Corp., which said last week that more than 1 million PlayStation 4 consoles had been sold in the 24 hours since its release.