Sources have said as many as 20 rockets could have landed at Hamid Karzai International Airport and in the surrounding area in Kabul.
Officials say the airport and immediate area was evacuated and all flights were cancelled.
Not details on casualties yet.
This comes just hours after US Secretary of Defense James Mattis and NATO chief Jens Stoltenberg arrived unannounced in Kabul for talks with Afghan officials.
Security forces closed off the area and officials said the Crisis Response Unit (CRU) was also called in.
At a joint press conference with US Secretary of Defence James Mattis and President Ashraf Ghani, NATO chief Jens Stoltenberg said Wednesday’s attack on Kabul airport was a sign of weakness on the part of the Taliban.
Mattis in turn called the rocket attack a crime.
Ghani meanwhile said that the CRU forces were at the scene and that the special forces had brought the attack under control.
Reports indicate security forces have been checking runways and have been clearing area of shrapnel after rocket attack.
The Taliban claimed responsibility for the attack and said the target had been Mattis.