IS said one of its fighters blew himself up at a "large gathering" in Kabul while others "detonated a parked explosives-laden vehicle" when security forces arrived, in a statement posted on the Telegram messaging app.
''I strongly condemn the inhumane attack on the wedding hall in Kabul last night. My top priority for now is to reach out to the families of victims of this barbaric attack. On behalf of the nation I send my heartfelt condolences to the families of those who were martyred,'' Ghani tweeted.
At least 63 people were killed and over 182 were injured following the attack.
Most of the injured were later taken to a hospital in the city.
According to eyewitnesses, the suicide bomber laid explosives among the wedding participants and detonated them.
People say that almost a thousand people were invited to the ceremony.
There are reports that this could end up being the deadliest attack on Kabul in recent times.
The blast happened in western Kabul, a predominantly Shia locality. The Shia minority has been targeted by the Taliban multiple times over the years.
These attacks come at a time when the United States are discussing a peace deal in Afghanistan, a deal that involves the Taliban giving up arms.