"She had been expelled," said the official at Cairo airport, adding that the former BBC journalist who hosted a political talk show on Egyptian TV was put on an EgyptAir flight to Beirut that left at 2130 GMT.
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Daoud's lawyer Zyad el Eleimi posted on Facebook that she had called him from the plane before the flight departed.
"Eight men who said they were from the border police force took her to an unknown location after taking her telephone and her British passport," Daoud's ex-husband Khaled al-Berri had earlier told AFP. Daoud also holds a Lebanese passport.
The men said they would check whether the journalist's residence permit was valid, and that she would otherwise face deportation.
The prominent TV talk show host's arrest came after her contract with Egyptian OTV television expired, Berri said.
Daoud has faced a barrage of online criticism in recent months over accusations she is close to the opposition to President Abdel Fattah al-Sisi's rule.
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Egypt's journalism union in May accused the authorities of declaring war on media freedom.
Earlier this month, the European Union called the indictment of three top journalists' union members "a worrying development."
Human rights activists accuse Sisi of running an ultra-authoritarian regime that has violently suppressed all opposition since toppling Islamist president Mohamed Morsi in 2013.
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