ERBIL, Iraq—Satellite photos obtained by the Associated Press confirm what church leaders and Middle East preservationists had feared: the oldest Christian monastery in Iraq has been reduced to a field of rubble, yet another victim of Islamic State group’s relentless destruction of heritage sites it considers heretical.

St. Elijah’s Monastery stood as a place of worship for 1,400 years, including most recently for U.S. troops. In earlier millennia, generations of monks tucked candles in the niches, prayed in the chapel, worshiped...