"Aisha gave birth very early this morning. She had a little girl. Mother and daughter are doing fine," said the official who spoke on condition of anonymity.
Dictator Gaddafi's second wife, Safia, daughter Aicha, and son had fled to Algeria earlier. According to the Algerian authorities, the Gaddafi family were allowed into the country on purely 'humanitarian grounds'.
"The wife of Muammar Gaddafi, Safiya, his daughter Aisha, and sons Hannibal and Mohammed, accompanied by their children, entered Algeria at 8:45 am (0745 GMT) through the Algeria-Libyan border," the foreign ministry said.
Libya's rebels are seeking the handover of Gaddafi's wife and three children and have criticised Algeria, which has not recognised the rebel National Transition Council, for allowing the family in.