Masked gunmen on a motorcycle fired shots at the back entrance of the Archangel Michael Church in Al-Fayoum's Sinnuras early on Tuesday.
The assailants escaped after the attack, which did not result in any casualties.
An eyewitness told the Egyptian television that the attackers fired random shots, adding that several residents of the neighborhood chased them in vain.
The residents reported the incident to the authorities who are now investigating it.
Egyptians began voting on a new draft constitution on Tuesday.