An Air Force C-130 J assigned to the 774th Expeditionary Airlift Squadron, part of the 455th Air Expeditionary Wing, crashed at Jalalabad Airfield, the Pentagon said.
Six US service members and five civilians on board died in the crash, it said.
The Pentagon did not immediately confirm the reason for the crash of the plane but the Taliban claimed responsibility for downing the aircraft.
"Our mujahideen have shot down a four-engine US aircraft in Jalalabad," Taliban spokesman Zabihullah Mujahid said on Twitter.
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The Taliban's claim of resposibility came as the hostility between NATO special forces and Taliban insurgents escalated in the northen Afghan city of Kunduz.
NATO-backed Afghan forces have been battling the Taliban over the control of Kunduz, which the insurgents captured on Monday.
The falling of the key Afghani city to the militants is seen as a game-changer for the Taliban that has been dogged by a leadership crisis since the July announcement of the death of its founder Mullah Omar.
Jalalabad, in eastern Afghanistan near the Pakistan border here many militants are based, is key to NATO-led military operations and has been the scene of several attacks recently.
Its airport is home to a major military base.
Taliban suicide bombers in December 2012 killed at least five people in an hours-long battle at the airport. It was the third attack on the airport that year.
The C-130 Hercules is a cargo plane built by Lockheed Martin. It is powered by four turboprop engines and is used extensively by the military to ship troops and heavy gear.