He said up to nine people were on the plane, which was heading to Arizona. Details of its mission have not been released.
"It's a sad day for the National Guard, and our thoughts and prayers are with the families of everyone involved and everyone with the National Guard as we work through this," Dahlen said.
The Savannah Professional Firefighters Association tweeted a photo showing the plane's tail end and a field of flames and black smoke as an ambulance stood nearby.
Only the tail section was still intact, said Chris Hanks, the association's assistant public information officer.
The tail section was sitting on Highway 21 and the ground in front of it was black and littered with debris, he said.
Savannah's Air National Guard base is the hub of recovery operations in Puerto Rico in the aftermath of hurricanes Irma and Maria.
Savannah/Hilton Head International Airport said the crash was affecting flights, although it happened off its property.
The Chatham County Emergency Management Agency tweeted that the National Guard cargo plane crashed on Wednesday at the intersection of two roads near the Savannah-Hilton Head International Airport.
Meanwhile, another Southwest Airlines flight had been forced to make an emergency landing with a broken window.
The plane from Chicago to Newark, New Jersey, was diverted for a "maintenance review" after the window cracked.
It follows the death of Jennifer Riordan, a philanthropist and Wells Fargo executive, who was partially sucked out a window von a Southwest Airlines plane less than three weeks ago. But passengers and even the President lauded Captain Tammie Jo Shults for safely landing the plane on April 17.
More to come