The Republican front-runner issued the threat adding people like the activist would be “carried out on a stretcher” during an event last night in Las Vegas, Nevada.
Describing the unnamed political opponent as “nasty as hell”, Mr Trump said: “I would like to punch him in the face, I”ll tell you.”
He claimed the man had been punching other people, though reporters in the crowd said there was no evidence of such a scuffle.
But an undeterred Mr Trump told the crowd of thousands: “See he”s smiling. See he”s having a good time.
“I love the old days, you know? You know what I hate. There”s a guy totally disruptive, throwing punches.
“We”re not allowed to punch back anymore. I love the old days.
“You know what they used to do to guys like that when they were in a place like this? They”d be carried out on a stretcher, folks.”
He praised the security guards who took the man out without hurting him.
Mr Trump continued: “It”s true. You know I love our police and I really respect our police and they”re not getting enough.
“They”re not. Honestly I hate to see that. Here”s a guy throwing punches. Nasty as hell.
“Screaming and everything else when we”re talking and the guards are very gentle with him, he”s walking out like big high fives. Smiling. Laughing. I would like to punch him in the face, I”ll tell you.”
Trump was speaking out ahead of the Republican caucus vote in Nevada, which will go to the polls on Tuesday.
The businessman, who owns a large stake in the Trump International Hotel, is the clear front-runner in the state.
A survey by CNN-ORC gave him 45 per cent, compared to 19 per cent for Ted Cruz and 17 per cent for Marco Rubio.
Nevada democrats held their caucus last week, which saw Hillary Clinton win with 52.6 per cent of the vote.