While Namibian officials declined Sunday to give any details on the birth Saturday of Shiloh Nouvel Jolie-Pitt, a doctor at the hospital said there were no complications and the mother and daughter were doing well.
"She is a healthy baby," the doctor said, speaking on condition of anonymity because he was not authorized to release information.
Police ringed the hospital with tight security Sunday, refusing to admit journalists and photographers into the building.
Pitt's publicist Cindy Guagenti announced the birth Saturday night, but said no other information or photographs would be released.
Samuel Nuuyoma, the governor of the Namibian region of Erongo, confirmed the birth at the Welwitschia Clinic in Walvis Bay and seemed to hint that key details would be released shortly.
"Any information relating to the birth of the baby will be made available to the public soon," said Nuuyoma, who has become friends with the celebrity couple.
The government has gone to extraordinary lengths to protect the privacy of Jolie and Pitt, who came to Namibia to avoid photographers and in the weeks leading up to the birth of their first child.
Namibia put tight security around their hotel and the hospital, set up large green barriers to protect their privacy from photographers and refused to grant visas to any foreign journalists unless they had written permission from Jolie and Pitt to cover the birth.
Police have also arrested photographers and confiscated film.
Speculation about the birth escalated Tuesday when Pitt sent an e-mail to the Cannes Film Festival that he was unable to attend the screening of his new film "Babel" because of the baby's "imminent arrival."
In "Babel," directed by Alejandro Gonzalez Inarritu, the 42-year-old Pitt plays a husband and father trying to cope with a crisis on vacation in Morocco. Cate Blanchett plays Pitt's wife, and the film also stars Gael Garcia Bernal.
"I am tremendously proud of `Babel' and want to congratulate everyone involved for this great achievement," Pitt said in the e-mail.
Jolie and Pitt were linked romantically shortly after appearing together in the 2005 movie "Mr. and Mrs. Smith."
Jolie, 30, is a frequent visitor to Africa and serves as goodwill ambassador for the U.N. High Commissioner for Refugees. She has two adopted children: toddler Zahara, from Ethiopia, and 4-year-old Maddox, from Cambodia. Both had their surnames legally changed to Jolie-Pitt after Pitt announced his intentions to adopt the children as well.
Pitt and actress Jennifer Aniston divorced last fall.
Jolie, who won an Oscar for her supporting role in 1999's "Girl, Interrupted," is divorced from Billy Bob Thornton and Jonny Lee Miller.