The incident occurred around 2 a.m. Tuesday at the huge airfield outside Kabul when two rockets landed at the facility, a U.S. Defense Department report said.
The C-17 plane that had brought the chairman of the Joint Chiefs of Staff to Afghanistan during the weekend was damaged, but Dempsey was never in any danger, and injuries to the airmen were not serious, the announcement said.
A NATO helicopter was damaged.
"The chairman was never in any danger from the attack, and there was no indication the insurgents targeted the general, officials said," the announcement said.
Separately, CNN quoted Dempsey's spokesman Col. David Lapan as saying the general was in his room on the base at the time of the incident.
"Two airmen suffered cuts and bruises, and the front of the transport jet and one engine were damaged," the Defense Department report said.
Military officials said the attack mimicked previous ones.
Dempsey, traveling by another plane, has since left Afghanistan to visit Iraq.
CNN quoted a security issue analyst as saying the Bagram incident again showed no place in Afghanistan is safe.
U.S. forces are scheduled to end combat operations in Afghanistan and leave by the end of 2014.