The US Secret Service confirmed one or more of its agents "opened fire on a gunman" located near the boundary of Trump's golf course, and that an "AK-47 style rifle" with a scope was recovered along with a GoPro video camera.
The suspect escaped in a black car but a witness helped police identify the vehicle and authorities tracked it down.
"We have somebody in custody right now that is a potential suspect," Palm Beach County Sheriff Ric Bradshaw told a press conference.
Trump had been golfing at his course in West Palm Beach, Florida, not far from his Mar-a-Lago residence, when the shooter was spotted a hole ahead of him, Bradshaw said.
"President Trump is safe following gunshots in his vicinity," his campaign spokesman Steven Cheung said in a statement.
The unnerving incident appears to mark the second time in as many months that Trump has been the target of a gunman. The former president was wounded in the ear on July 13 as he was speaking at an outdoor rally in Butler, Pennsylvania.
Authorities who addressed Sunday's press conference did not confirm whether a gunman actually fired in the direction of the former president, but Secret Service agents did engage the suspect.
"We are not sure right now if the individual was able to take a shot at our agents," said Rafael Barros of the Secret Service.
'Rifle barrel sticking out'
The Federal Bureau of Investigation said it is "investigating what appears to be an attempted assassination of former President Trump."
Sheriff Bradshaw said Secret Service personnel doing protective work on the course as Trump played golf spotted "this rifle barrel sticking out of the fence and immediately engaged that individual, at which time the individual took off."
He said the suspect was set up probably between 300 and 500 yards (275 to 455 meters) away, but "with a rifle and a scope like that, that's not a long distance."
Sheriff William Snyder of neighboring Martin County said on CNN that the potential suspect who was stopped by law enforcement had "a relatively calm, flat affect. He was not displaying a lot of emotions."
Law enforcement were launching a sweeping investigation and intense focus will come down on the arrested suspect, but as of Sunday afternoon there was no indication of a motive for the attempted assassination.
The incident came amid heightened concern for the safety of both candidates.
The White House quickly issued a statement saying both President Joe Biden and Vice President Kamala Harris, Trump's Democratic rival in the November election, had been briefed about the incident.
"They are relieved to know that he is safe," the statement said.
Harris herself responded to say she was relieved a tragedy was avoided.
"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," she said. "Violence has no place in America."
The US Secret Service, tasked with protecting presidents, former presidents and other dignitaries, faced criticism after the Pennsylvania incident.
Kimberly Cheatle, the head of the agency, resigned amid the ensuing scrutiny, and at least five Secret Service agents were placed on administrative leave.
Cheatle acknowledged in her letter of resignation that the agency "fell short" of its mission to protect the nation's leaders.
