The Afghan soldier reportedly killed himself following the incident.
Abdul Rahim Wardak, Afghanistan's defence minister, said he was "saddened and deeply regretful this tragedy occurred," vowing a full investigation.
Afghanistan has seen rising violence in recent years as Taliban forces - ousted from power by a US-led invasion in 2001 - reorganise and launch attacks from the border region with Pakistan.
Barack Obama, the US president, unveiled a new "comprehensive" strategy for the war in Afghanistan on Friday following a review of policy in the region.
The US has about 38,000 troops in Afghanistan, in addition to the 17,000 US forces Obama ordered to be deployed in February and around 42,000 Nato troops.