The pilot and passenger of the Cessna were killed in the collision. The coroner for Berkeley County, where the collision took place, is expected to announce the victims' names during a news conference at noon Wednesday.
Col. Stephen Jost, commander of the 20th Fighter Wing at Shaw, said Johnson appeared to be unharmed, but was taken for a medical evaluation as a precaution.
The Federal Aviation Administration said the jet collided with a Cessna C-150 around 11 a.m. Tuesday about 11 miles north of Charleston, in an area known as Moncks Corner next to the Cooper River. The National Transportation Safety Board said it is investigating the crash, along with a standard Air Force investigation board.
Johnson was flying a routine instrument training mission at the time of the incident and was on approach to Joint Base Charleston, Jost said.
The plane was not carrying any ammunition or ordnance at the time, he said.
"In my experience, I haven't had any close calls because the Air Force is very disciplined about how it operates its aircraft," Jost said. "We don't do our tactical maneuvering until we're in assigned military operating areas or warning areas out over the water."
Jost said authorities would have a better idea of what happened during the accident once flight data from the F-16 wreckage is recovered.
According to Bill Salisbury of the Berkeley County Rescue Squad, the Cessna aircraft left the Berkeley County airport just a few minutes before the crash. The plane was likely headed toward Myrtle Beach, and was in radio contact with the county airport during its flight, he said.
"Our thoughts are with the friends and family of anyone aboard the civilian aircraft," Shaw said in a statement.
The Coast Guard's 7th District confirmed that a MH-65 rescue crew from Savannah, Ga., responded to the incident. Video posted to a Pentagon website shows the crew approaching the crash site. The Coast Guard said a rescue swimmer was deployed to help the downed pilot.
Berkeley County officials said most of the wreckage from the crash landed in an almost seven-and-a-half mile uninhabited area through swampland and rice fields.
But some wreckage did crash down in populated areas, including a nearby mobile home park.
Pictures posted online showed an engine similar to an F-16's General Electric F110 as part of wreckage, leaning up against a mobile home. Local Charleston TV station WCBD reported that the family who owned the trailer were out of town at the time.
Officials said they do not believe anyone on the ground was injured because of the crash. Shaw is urging those near the wreckage of the crash to call 911, and those with claims of damage to contact the base's legal office.
Additional wreckage in a wooded area showed the tail of the F-16, with the "55" and two dice flash of the 55th Fighter Squadron at Shaw.
Local Charleston TV station WCBD quoted a witness as saying he saw two planes collide in the air, causing a "ball of fire."
North Charleston Fire Department spokeswoman Bianca Bourbeau told The Associated Press that her agency has sent a chief and a marine unit to assist Berkeley County with a reported plane crash, and will send other help as needed.
Officials from the Air Force, NTSB, and Berkeley County, S.C., where the crash took place, have scheduled another news conference for noon on Wednesday to provide further updates.