The attack on the main military airfield in Afghanistan took place on Tuesday evening and the nationality of the service member could not immediately be released, a Nato official said.
The Nato statement did not identify which militant group was responsible for the attack, though most of the groups active fall under the broad umbrella of the Taliban
Read: Afghan Taliban seize Humvees for sneak attacks and propaganda
Bagram air base, which is guarded by US Marines and partnered forces, frequently comes under rocket attack from militants. Fighting in Afghanistan has escalated since most foreign forces withdrew from last year and Afghan forces are bearing the brunt of the conflict.
A Taliban government was ousted by a US-led coalition in 2001 and its militants have been waging an increasingly violent insurgency for over a decade.
On Tuesday alone, at least 25 members of the Afghan army and police were killed in clashes, an interior ministry report showed. The Nato coalition has lost nine members of its force this year.
Read: At least six Pakistanis killed in clash with Taliban militants near border with Afghanistan
Around 13,000 Nato troops are engaged in a new two-year training mission. In addition, several thousand US military personnel are still engaged in combat duties but details of their operations have not been disclosed.
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