"The attack began loudly," Fereidon-Kawazoun, a spokesman for Abdullah, said, "It appears that a missile landed in the area. Abdullah and some other politicians have left without being harmed."
The Afghan "Talao" channel showed live pictures of people running in search of protection while hearing the shooting.
Interior Ministry spokesperson Nusrat Rahimi said that special police forces had been sent to the area.
It was not immediately clear who was behind the attack, or whether there were any injuries.
For his part, the Afghan President, Ashraf Ghani, condemned the attack on the ceremony, stressing that it was a "crime against humanity".
US and Afghan officials had previously said that the United States and its NATO allies would withdraw their forces from Afghanistan within 14 months, if the Taliban fulfilled their obligations under an agreement signed in the Qatari capital, Doha.