In the statement, the terror group said that two IS-K suicide bombers carried out the attack on Friday inside the Bibi Fatima Shia mosque in the city's police district one (PD1) when hundreds of worshippers were offering prayers, Khaama Press reported.
The statement said that the first suicide bomber detonated his explosives in the hallway of the mosque and while the second did it inside.
Initial reports had said that there were three suicide bombers who shot at security guards of the mosque and then entered and detonated their explosive vests.
It is the second deadly attack by the group in the past two weeks targeting the Shia Muslims in Afghanistan.
Friday's attack came exactly after a week when another Shia mosque in Kunduz city was hit by a suicide bombing which claimed the lives of at least 50 people.
The IS-K had claimed responsibility for the attack, which was the deadliest since the US forces left Afghanistan at the end of August.
Earlier this week, Russian President Vladimir Putin had said that a large number of IS militants have been entering Afghanistan which can threaten the security of Central Asian countries.
The Taliban, which took over Afghanistan in August, said the IS were only making trouble but were not a threat.