She said 22 people, including two crew members, survived the accident, 18 of whom were hospitalised with injuries.
The Boeing-737 is thought be locally owned but operating a service to Tehran on behalf of an Iranian carrier.
Local officials say most of the passengers were either Iranian or Kyrgyz.
The cause of the crash was not known but reports from the scene said the jet came down shortly after takeoff and may have been trying to make an emergency landing.
The crew had reported a technical problem about 10 minutes into the flight, an airport official said.
The US military has bases in the area to support its operations in Afghanistan and it sent rescue personnel and equipment to help deal with the disaster.