The device reportedly detonated as officers checked the suspicious item.
One Egyptian police officer was killed while another was injured in the explosion, Sky News Arabia said. There was no immediate claim of responsibility.
The incident occurred less than two days ahead of the 7 January Coptic Christmas celebrations in Egypt. Christians reportedly account for some 10 percent of Egypt's largely Muslim population.
The Egyptian television reported that the country's prosecutor's office had launched an investigation into the incident. Police cordoned off the area near the church and are searching the neighborhood.