No one was injured in the accident, which happened at about 4 p.m.
Jesse Morton, an employee of the golf course, said he watched the plane come down.
"I was on the phone and I just happened to turn around and saw it spinning," Mr. Morton said.
Becky Shealy, the vice president of business development for the Daniel Field-based Augusta Aviation Inc., said officials aren't sure how the single-engine Cessna 172 crashed but that the pilot appeared to lose control at some point during the landing. She said both occupants were up and walking around after the wreck.
"What a way to start Masters Week," Ms. Shealy said.
The airplane is owned by a customer of Augusta Aviation, she said.
Airport Director Buster Boshears said it appears the plane "landed long" and went through the fence.
The Federal Aviation Administration has been notified of the accident and will investigate, Ms. Shealy said.
Tuesday's landing problem is the second one at an Augusta airport this week.
On Sunday, a Beechcraft King Air C-90 landed on its belly at Augusta Regional Airport when it experienced landing gear failure.
No one aboard the private twin- turboprop was injured, but operations at Augusta Regional were halted for about 80 minutes while crews cleaned up.
Reach Adam Folk at (706) 823-3339 or firstname.lastname@example.org.