Al-Shafei Mohamed, a police investigator in Luxor, says the girl's father, a wealthy businessman, reported the kidnapping Saturday.
Ahmed Hassan, a family friend, says the 4-year-old girl and her 20-year-old female cousin were kidnapped during a family celebration Friday night. He said it was unclear who carried out the kidnapping.
Kidnapping for ransom is uncommon in Egypt. But hundreds of people go missing every year, and many of the cases go unsolved.
Luxor, where the kidnapping took place, is a famed ancient city known for its pharaonic temples.