A policeman was killed and another injured as gunmen fired shots at the Virgin Mary Church in 6 October City in Giza.
According to the MENA news agency, there were five gunmen involved in the shooting.
Security services arrested one of the gunmen, while the rest are being pursued, a security source said.
The source added that the remaining gunmen were in a car and that several officers were set to arrest them.
The security source also told Al-Masry Al-Youm that the identity of the arrested gunman is being checked to confirm his involvement .
Egyptian Copts are estimated to be 10 percent of Egypt's population. Sectarian strife has increased since the 2011 revolution and resulted in several incidents between opposing sides.
Edited translation from MENA