According to Egypt's Interior Ministry, security forces followed an escape route used by attackers who targeted St Catherine's Monastery in southern Sinai, before killing the suspect in a shoot-out on Wednesday.
Islamic State said it was behind the fatal shooting of a police officer at a checkpoint approximately 800 metres from the Eastern Orthodox site on Tuesday.
It happened just over a week after 45 people were killed in two suicide bombings at Coptic churches in Alexandria and Tanta on Palm Sunday.
The incident happened ten days ahead of a schedule visit by Pope Francis to Egypt.
According to Reuters, Egypt's Interior Ministry said police involved in the death of the suspect also found an automatic weapon and ammunition.