The 31-year-old Russian supermodel, who has been dating Cooper, 42, since spring 2015, gave birth two weeks ago, reported People magazine.
However, no other details were made available.
Shayk's pregnancy news came out in November after she showcased a baby bump while walking the runway at the 2016 Victoria's Secret Fashion Show.
The two were first romantically linked in May 2015 when they were spotted kissing in New York City.