Al-Qaeda-linked group attacks Camp Simba, a base used by US and Kenyan military personnel, in Lamu County.
The US military command for Africa, AFRICOM, confirmed there had been an attack in a brief statement.
"U.S. Africa Command acknowledges there was an attack at Manda Bay Airfield, Kenya and is monitoring the situation. Al-Shabaab has claimed responsibility for the incident. As facts and details emerge, we will provide an update."
Earlier, al-Shabab said in a statement the raid resulted in "severe casualties on both American and Kenyan troops stationed there."
"The Mujahideen fighters covertly entered enemy lines, successfully stormed the heavily fortified military base and have now taken effective control of a part of the base," the armed group said.
The attack sent a dark plume of smoke into the air, Abdallah Barghash, a witness, told Reuters news agency. Barghash was among the crowds watching the drama unfold on Manda Island from neighbouring Lamu Island, a top tourist destination.
Al Jazeera's Haru Mutase, reporting from Kenyan capital, Nairobi, said it was an audacious attack by the armed group.
"The base is heavily fortified and al-Shabab still managed to break through. We are told the actual attack is over and that Kenyan and American forces are combing through the area trying to find those responsible," Mutasa said.
"The area is near Boni forest where al-Shabab is thought to operate from. In the past, Kenyan security forces have been going in and out of that forest to try to weed out al-Shabab fighters," she added.
Al-Shabab has maintained a campaign of deadly bomb and gun attacks despite being ejected from their bases in the Somali capital, Mogadishu, and other areas years ago.
Source: Al - Jazeera