Doral Police department said officers responded to the call at the resort in the early hours of Friday morning.
Doral police said in a tweet that they had taken one individual into custody, but that nobody was found with injuries at the Trump National Doral Miami resort.
Police did not confirm reports that the suspect was injured during his interaction with officers.
"We don't know what his intentions were in the long term but we know what he was doing at the time - he was trying to engage our police officers in some kind of ambush-type attack", Perez said.
According to the Doral Police Department, one officer was wounded in a confrontation with a lone gunman who was then arrested.
Perez said that it was too early to speculate on the man's motives.
Perez did not provide details on what the shooter was saying about Trump, who was at the White House at the time.
The fire alarm was blaring, which Perez said was an attempt by the suspect to lure officers into the lobby.
Police were notified of an "active shooter" in the Trump-owned club about 1:30 a.m. ET, Doral Police Chief Hernan Organvidez told news reporters.
"In my opinion, they probably saved a hell of a lot of lives today, because this could have gone a lot worse", Perez told 610 WIOD.
Homeland Security and Secret Service agents are on the scene, and the Federal Bureau of Investigation is en route, Perez said. Police from Doral and Miami-Dade quickly encountered him and exchanged gunfire.
In a statement, the Secret Service says no one under their protection was affected by the shooting at the resort near Miami that's owned by President Donald Trump. The entrances were blocked, and yellow caution tape was stretched across the main gate.
The golf resort previously known as the Doral Resort & Spa was purchased by the Trump Organization in 2012. The massive property has four courses - its most signature being the Blue Monster, which has hosted numerous PGA Tour and World Golf Championships events featuring the world's top golfers. Authorities said they do not believe he was a guest at the 800-acre golf resort in the city of Doral, about 15 miles northwest of downtown Miami.