Farida Gamal Hosni Mubarak was the first child born to Mubarak, 46, seen as a potential successor to his father, and his wife Khadija el-Gammal.
President Hosni Mubarak, 81, is recovering in a German hospital after having his gallbladder removed earlier this month. The medical team treating him at Heidelberg University Hospital said he had benign tissue removed.
Members of his family have been by his bedside regularly, but the agency did not say where the baby girl, the president's first granddaughter, was born nor whether Gamal Mubarak was at the birth.
Mubarak has not said if he will run for a sixth six-year term in the 2011 presidential election. Many Egyptians believe that, if he does not, he will try to hand power to his politician son. Both Mubaraks deny any such plan.