The militants claim they have shot down the drone in Laghman Province and say they have collected the ruins Press TV reported.
Officials have not yet confirmed the report.
Earlier, another US spy drone crashed in Ghazni Province.
Afghan soldiers reportedly found the wreckage of the crashed drone and handed it over to the US-led forces in the region.
On Thursday, an American helicopter belonging to the NATO-led International Security Assistance Force (ISAF) also crashed in the eastern province of Khost. The cause of the crash was not determined.
The Taliban militants claim they have shot down several unmanned aircraft and NATO choppers in different parts of Afghanistan.
The US frequently uses surveillance as well as armed drones to launch airstrikes in Afghanistan and elsewhere.
Source : Afghan Voice Agency (AVA), International Service