"She has arrived and words fall short to express our happiness. Thank you for all your wishes," Shahid tweeted.
Mira was admitted to the Hinduja Healthcare Surgical Hospital in suburban Khar on Thursday.
Earlier the child was expected to be born sometime around mid-September. A hospital source said the delivery was normal and the mothers as well as the child were doing fine.
Mira had been spotted with a baby bump at the Lakme Fashion Week in Mumbai in April, while Shahid revealed during the trailer launch of Udta Punjab that he was going to become a father.
The couple had tied the knot in July last year. It was an arranged marriage.
Shahid will soon be seen in Vishal Bhardwaj's period drama Rangoon.