The rockets were launched from the surrounding areas in the vicinity of the airport, some Afghan media sources said, IRNA reported.
The incident comes after the US Defense Secretary Jim Mattis arrived in the country.
There has been no report on the possible casualties and damage of the strike.
Some online media said that at least 20 rockets have landed at the airport.
Afghanistan Interior Ministry spokesman Najib Danesh on his Twitter page confirmed the attack on the Kabul airport, but said that there were no damage or casualties. Danesh also said that the flights are underway as scheduled.
The Taliban terrorist group spokesman Zabihollah Mojahed on his Telegram channel claimed the responsibility of the rocket attack. He also claimed that the rockets hit the Afghan and foreign forces base, and have inflicted major damage and casualties.
Matis who is visiting southern Asia, after his day-long trip to India, arrived in Bagram Airfield, in eastern Kabul Wednesday morning.