One of its fighters carried out the suicide attack on the Coptic Christian cathedral, the group said in a statement.
Egyptian President Abdul Fattah al-Sisi had earlier named the attacker as Shafik Mahmoud Mohamed Mostafa, 22.
Mr Sisi said the attack caused "pain to all Egyptians".
IS named the attacker as Abu Abdallah al-Masri.
President Sisi used his address at a service for victims on Monday to urge the government to amend the country's terrorism laws, which he said were "restricting the judicial system" in its battle to prevent such attacks.
He also declared three days of national mourning for the victims of the blast.
The Christian minority in Egypt has frequently been targeted by Islamist militants.
Egypt has seen a wave of attacks by militants since 2013, when the military overthrew President Mohammed Morsi, an elected leader who backed the Muslim Brotherhood, and launched a crackdown against Islamists.
Some of Mr Morsi's supporters blamed Christians for supporting the overthrow.
So-called Islamic State say it was behind a bomb attack on a church in Cairo on Sunday in which at least 25 people were killed.