The superstar rapper, 37, said she is “madly in love” with the new arrival and thanked her celebrity friends for sending their congratulations.
She shared snaps of messages from famous faces including Beyonce, Kim Kardashian West and fashion designer Riccardo Tisci.
Minaj, who married partner Kenneth Petty in 2019, wrote on Instagram: “Thank you to Queen B, Kim & Ye, Riccardo Tisci, Winnie, Karol & everyone who sent well wishes during this time.
“It meant the world to me. I am so grateful & in love with my son. Madly in love. My favourite liddo boy in the whole wide world.”
The handwritten note from mother-of-three Beyonce read: “Onika, Welcome to motherhood. God bless you and your family. B.”
And the message from Kardashian West and husband Kanye, who have four children, read: “Congrats! We love you! Kim + Kanye.”
Canadian model Winnie Harlow also congratulated Minaj.
Chart-topping rapper Minaj, whose hits include Super Bass and Anaconda, announced she was pregnant in July.
Alongside a picture of her cradling her bump while wearing a floral bikini and high heels, Minaj wrote on Instagram: “#Preggers.”