An AK-47-style rifle with a scope and a GoPro was discovered in the bushes and two backpacks were hung on the fence, Sheriff Ric Bradshaw told reporters.
“Fortunately, we were able to locate a witness that came to us and said, ‘Hey, I saw the guy running out of the bushes,’” he said.
“He jumped into a black Nissan, and I took a picture of the vehicle. We have somebody in custody right now that is a potential suspect.”
Sheriff Bradshaw said the GoPro pictures were being processed.
“The Secret Service agent that was on the course did a fantastic job,” he said.
“What they do is they have an agent that jumps one hole ahead of time towards where the President was at and he was able to spot this rifle barrel sticking out of the fence and immediately engaged that individual at which time the individual took off.”
Police will release the suspect’s name and picture when he is booked into county jail and charged, Sheriff Bradshaw said.
Mr Trump told Fox News host Bret Baier that he was playing on the fifth hole when the shots rang out.
He said he was fine and there was no evidence any shots were near him or hitting near him.
He was put in a golf cart and quickly driven away back to the clubhouse.
“Tell everybody I am fine and the Secret Service did a great job,” Mr Trump said.
A source told The Daily Mail the fifth and sixth hole was a “vulnerable” area as it is one of the parts of the course closest to the road and the undergrowth is cut back every summer.
The man was spotted by a Secret Service advance team in front of Mr Trump, per the NY Post.
The golf club is close to Mr Trump’s Mar-a-Lago home.
“The Secret Service, in conjunction with the Palm Beach County Sheriff’s Office, is investigating a protective incident involving former President Donald Trump that occurred shortly before 2pm,” said Secret Service spokesman Andrew Guglielmi.
“The former President is safe.”
Mr Trump declared “I AM SAFE AND WELL” in a fundraising email following the incident.
“There were gunshots in my vicinity, but before rumors start spiraling out of control, I wanted you to hear this first: I AM SAFE AND WELL!” the email said. “Nothing will slow me down. I will NEVER SURRENDER! I will always love you for supporting me.”
According to Fox News host Sean Hannity, Mr Trump was golfing with donor Steve Witkoff at the time.
“The first thing the President did when he got back to the clubhouse was make sure everybody else was OK,” Hannity said he was told by Mr Witkoff.
The incident comes two months after Mr Trump was shot in the ear in an assassination attempt at a rally in Pennsylvania that left one man dead and two other attendees injured.
The White House said Joe Biden and Kamala Harris had been informed.
“The President and Vice President have been briefed about the security incident at the Trump International Golf Course, where former President Trump was golfing,” a spokesman said.
“They are relieved to know that he is safe. They will be kept regularly updated by their team.”
Ms Harris said in her own statement on X, “I have been briefed on reports of gunshots fired near former President Trump and his property in Florida, and I am glad he is safe. Violence has no place in America.”
The Martin County Sheriff’s Office said the northbound I-95 had been shut down.
“Based on BOLO [be on the lookout] information released by Palm Beach County, the Martin County Sheriff’s Office has stopped a vehicle and taken a suspect into custody believed to be connected to a shooting incident at Trump International in Palm Beach County,” police said in a Facebook post.
“We will update this information as it becomes available.”
Trump spokesman Steven Cheung said earlier on Sunday afternoon, “President Trump is safe following gunshots in his vicinity.”