Police had arrested one member of the cell who led them to their mountain hideout in the southern province of Qena where the two other extremists opened fire on Tuesday, the ministry said.
The two suspects, who had not been identified, were killed in the ensuing firefight, along with the informer and a police officer guarding him.
Egypt is battling a local affiliate of ISIS, which had claimed attacks that had killed more than 100 Copts since December.
At the hideout, police found weapons and "gold jewelry which was probably stolen from some of the Christian victims" of a massacre earlier this year.
On May 26, Daesh gunmen killed 29 Copts as they travelled in a bus to Saint Samuel monastery in Minya province south of the Egyptian capital.
The bus attack followed two suicide bombings of churches in April that killed 45 Copts. In December, a suicide bomber struck a church in Cairo, killing 29 Copts.
Copts make up about 10 percent of Egypt's 90-million population.
Egypt's ISIS affiliate is based in North Sinai province, where hundreds of soldiers and policemen had been killed in attacks since the military's ouster in 2013 of President Mohamed Morsi.