Eyewitness footage from the scene shows Abdullah interrupted during a commemoration ceremony for the killing of Abdul Ali Mazani, a leader of the predominantly Shiite Hazara ethnic group in 1995, RT reported.
"The attack started with a boom, apparently a rocket landed in the area, Abdullah and some other politicians ... escaped the attack unhurt," eyewitness Fraidoon Kwazoon said.
Meanwhile, Afghan President President Ashraf Ghani called it a “a crime against humanity and against the national unity of Afghanistan.”
No group has claimed responsibility for the assault yet.