Pentagon press secretary Peter Cook said the fighter from the 455th Air Expeditionary Wing crashed around 8:30 pm (1630 GMT).
"Coalition forces are securing the crash site. The cause of this accident will be investigated," Cook said.
The Taliban said their fighters shot down the jet, claiming that all on board had been killed. The insurgent group is well known for exaggerating battlefield claims.
Cook said there was no immediate indication the plane came down due to enemy action.
The pilot safely ejected and was recovered by coalition forces, and was being evaluated by medical personnel.
Bagram is the largest US military base in Afghanistan and is located north of Kabul.