Afghan officials say he was one of about 120 suspected militants killed in an operation in Kot district.
It comes days after a bomb attack in Kabul claimed by IS killed 80 people.
Emarati was formerly a Taliban commander, but switched allegiance to IS following the death of Mullah Omar, the Taliban founder.
Analysts say he was one of the most important leaders of IS in the region, and that his death, if confirmed, would be a serious setback to the group`s ability to operate in eastern Afghanistan.
Afghan officials have released photos following the overnight raid in Kot, showing IS courts and recruitment centres seized by the military.
Afghan special forces commander Gen Basmullah Wazari said the operation had received foreign air support.
Emarati was one of the first militant commanders in the Afghanistan-Pakistan region who pledged allegiance to IS`s leader Abu Bakr al-Baghdadi.
He was a former Afghan Taliban commander in central Logar province who was sidelined and disarmed by the Taliban leadership for "unauthorised activities" in 2013.
After that, he spent time with the Pakistani Taliban (TTP), and, on 12 January 2015, appeared in a video with two other Afghan Taliban commanders, and nine ex-TTP commanders, pledging allegiance to IS.
Two weeks later, IS announced the establishment of its branch in "Khorasan" - an old name for Afghanistan and parts of neighbouring Pakistan, Iran and Central Asia - and Emarati became one of its most important commanders.
After the IS`s Khorasan branch established its base in the eastern Nangarhar province of Afghanistan, Emarati led several attacks against the Afghan Taliban and government forces to expand the new group`s control and influence. He was accused of kidnapping for ransom among other actions and was known for his ruthlessness.
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