Iranian officials said they had arrested a gunman who carried out the attack at the Shah Cheragh shrine in the city of Shiraz. State media blamed takfiri terrorists - a label Tehran uses for hardline Sunni Muslim militants like Islamic State.
The group has claimed previous attacks in Iran, including deadly twin bombings in 2017 which targeted Iran's parliament and the tomb of the Islamic Republic's founder Ayatollah Ruhollah Khomeini.
Wednesday's killing of Shi'ite pilgrims came on the same day that Iranian security forces clashed with increasingly strident protesters marking the 40-day anniversary since the death in police custody of Mahsa Amini, a 22-year-old Kurdish woman.
Interior Minister Ahmad Vahidi blamed the protests sweeping Iran for paving the ground for the Shiraz attack, and President Ebrahim Raisi said Iran would respond, according.
"Experience shows that Iran's enemies, after failing to create a split in the nation's united ranks, take revenge through violence and terror," said Raisi, speaking before Islamic State released its claim of responsibility.
"This crime will definitely not go unanswered, and the security and law enforcement forces will teach a lesson to those who designed and carried out the attack."
The semi-official Tasnim news agency said the attacker shot an employee at the shrine entrance before his rifle jammed and he was chased by bystanders.
He managed to fix his gun and opened fire on his pursuers, before entering a courtyard and shooting worshippers. Several women and children were among the dead, it said.
