The explosion occurred when the bomber detonated their vest inside a mosque in the sixth police district of Kabul, according to Basir Mujahid, spokesman for the local police force.
Mujahid told CNN that children and women were among the victims.
ISIS claimed responsibility via a statement published by its media wing, Amaq news agency.
The statement said that it targeted the Shia gathering in Kabul but did not disclose any information on the identity of the suicide bomber.
The attack took place at 12:10 p.m. (2:40 a.m. ET) after a suicide attacker entered Shia mosque Baqir ul-Uloom as religious worshipers gathered to mark the Shia ceremony of Arbaeen, which comes 40 days after the major festival of Ashura.
Ashura commemorates the martyrdom of Hussein, the grandson of the Prophet Muhammad who was killed in the year 680 AD.
Taliban spokesman Zabiullah Mujahid has denied the group is responsible for Monday's attack.
"This appalling attack on worshipers is an atrocity," Pernille Kardel, the UN Secretary-General's deputy special representative for Afghanistan, said in a statement.
"UNAMA expresses its revulsion at this latest effort by extremists to stoke sectarian violence in Afghanistan," said Kardel, who is also the acting head of the United Nations' mission in Afghanistan.
"Religious and ethnic tolerance are values the Afghan people hold strong, and I urge the Afghan authorities to do everything possible to defend Afghans of all faiths," she said.
The US embassy in Kabul also condemned the attack, calling it a "senseless and cowardly" act.
"This attack is another demonstration of contempt for religious tolerance and communal harmony by the enemies of peace and progress in Afghanistan," the embassy said in a statement.
Spate of violence
Last week a suicide attack near the Defense Ministry in Kabul
killed four people and wounded 11, the latest in a series of attacks which have come around the 15th anniversary of the 9/11 terror attacks and the beginning of the subsequent US "war on terror."
The Taliban claimed responsibility for that strike, praising the "strong attack" on Bagram Airfield in a tweet.
In a statement, Mujahid said a suicide bomber had targeted "a sports ground where more than 100 military officers, important people and soldiers were busy exercising."
In the same week, a suicide attack targeting the German consulate in northern Balkh province killed four others.