The statement reads, "A security source told Amaq that the attack had been executed by militants of IS" unlike its previous statements that explicitly claimed responsibility for the group's attack.
Located at the foot of Mount Sinai, St Catherine's is one of the oldest Christian monasteries in the world and a Unesco world heritage site.
Islamic State claimed responsibility for the attack on a police checkpoint about 800 metres from the entrance to the monastery, one of the world's most important Christian sites.
Tuesday's attack comes just days after bombings at two Coptic Christian churches left 45 people dead.
St Catherine's monastery, which lies some 500 kilometres (300 miles) southeast of Cairo in the south of the Sinai peninsula, attracts thousands of visitors a year.
Mark Hamill: Carrie Fisher Star Wars tribute is 'therapy'
It looks like classes are back and they're better than ever! In the distance, albeit quite small, you will see a familiar sight. He was fathered by a traitor-by the chosen one who betrayed the Jedi, destroyed its entire infrastructure, and joined the Sith.
In February, scores of Christian families and students fled North Sinai province after a spate of targeted killings.
The shooting occurred at a security checkpoint, the source said, but it was not immediately clear who had opened fire.
An Islamist insurgency has gained pace in northern Sinai since President Mohamed Mursi of the Muslim Brotherhood was overthrown as president in 2013. The extremist group has lately stepped up its attacks, moving its activities from Sinai to other parts of Egypt and is increasingly using sophisticated tactics that are likely to fuel sectarian tensions and embarrass el-Sissi.
It comes shortly before a planned visit by the Vatican Pope Francis to Egypt next week.