The attack on Thursday killed Abdul Rahman, identified by the US military as the Kunar provincial emir for Islamic State of Iraq and Syria-Khorasan, according to a statement from the command in Kabul.
Nicholson has vowed to defeat Islamic State militants in Afghanistan this year.
In April, Nicholson deployed a 21,600-pound (9,797 kg) "Massive Ordnance Air Blast" bomb against Islamic State positions in neighboring Nangarhar province, one of the largest conventional weapons ever used by the United States in combat.
As part of an increased campaign against both Islamic State and the Taliban, the dominant Islamist militant group in Afghanistan , the US Air Force has dropped nearly 2,000 weapons in the country as of the end of July, compared to fewer than 1,400 in all of last year.
Despite some battlefield successes by Afghan and American special operations troops, Islamic State has continued deadly attacks around Afghanistan , fueling fears that the group is seeking to bring the group's Middle East conflict to Central Asia.