"The bombing was carried out by a woman named Fatima. The bombing was in retaliation for the insult to our Prophet," he said.
The attack came a day after protests turned violent for the first time in Afghanistan over "Innocence of Muslims", as hundreds of angry men hurled stones at a US military base, clashed with police and shouted "Death to America".
The movie, believed to have been produced by a small group of extremist Christians, has sparked a week of furious protests outside US embassies and other American symbols, killing 19 people in at least 20 countries before Tuesday's bombing.
Hezb-i-Islami is Afghanistan's second-biggest insurgent group after the Taliban and is led by Gulbuddin Hekmatyar, a former prime minister.
Earlier this year, he told the Afghan Islamic Press news agency that he was ready for meaningful talks with all parties to end the decade-long war in Afghanistan, but was dismissive about the results of contacts he said had already been had with Washington and the Afghan government.
Hekmatyar, a marginalised Afghan warlord whose party was first established in the 1980s to resist the Soviet occupation of Afghanistan, leads thousands of fighters in the east and northeast of the country.