People magazine said McCartney and her husband, Alashair Willis (search), announced the birth of their first child, born early Friday morning.
"Both mother and father are thrilled with the news," the couple's representative told the magazine.
McCartney, 33, married Willis in August 2003. Willis, 34, is a former magazine publisher.
Despite her pregnancy, McCartney managed to put together a new collection, to be unveiled in Paris next week. "Stella worked on and was able to complete the collection before giving birth," People quoted her publicist as saying.
The show will go on, but it wasn't known whether McCartney would be able to attend.