According to euronews, there were no reports of American or or Kenyan deaths at Camp Simba, in Lamu county near the Somali border.
The camp has under 100 US personnel, according to Pentagon figures.
A statement by the US Africa Command said the Manda Bay airfield "is still in the process of being fully secured" and described the situation as "fluid."
A plume of black smoke rose above the base after the attack. Kenya's military said at least four attackers were killed.
United States Africa Command spokesman Col. Christopher Karns confirmed the attack but called al-Shabab's claims to have inflicted severe casualties were “grossly exaggerated.”
A Kenyan police official said five suspects had been arrested.
A Kenyan police report seen by the Associated Press said two fixed-wing aircraft — a US Cessna and a Kenyan one — were destroyed along with two US helicopters and multiple US vehicles.
MNA/PR