The drone attacks in Nangarhar's remote Achin district hit the "Voice of the Caliphate" station operated by IS, officials said.
IS expanded into Afghanistan last year, and began an FM radio station in an effort to attract new recruits.
They have clashed with Afghan forces, as well as rival Taliban militants.
IS members have also killed numerous local people, who tell stories of horrific violence.
The air strikes took place from 19:00 to 20:00 local time (14:30 to 15:30 GMT) on Monday, a spokesman for Nangarhar province, Attaullah Khogyani, told the BBC's Mahfouz Zubaide.
There were a total of four drone strikes, which hit the radio station, an internet control centre and other IS targets, he added.
Twenty-one IS members, including five operating the radio station, were killed, reports said.
The "Voice of the Caliphate" station had been broadcasting in Pashto, Dari and Arabic, carrying anti-government propaganda and calls for young Afghans to join Islamic State.
Radio is the main source of entertainment and news in Afghanistan, which has more than 170 radio stations.
The Islamic State group announced an offshoot in Afghanistan in January 2015, sparking a conflict with the Taliban.
The Taliban say they have set up a "special forces" unit with more than 1,000 fighters that aims to crush IS.
Last month, Afghan President Ashraf Ghani vowed to "bury" IS, telling the BBC that the group's atrocities had "alienated the people".
US air strikes in eastern Afghanistan have destroyed a radio station used by the Islamic State militant group, US and Afghan officials say.