Wellington Field Crime Manager Detective Inspector Darrell Harpur said this afternoon police had worked "under urgency" in the lead-up to today's arrest.
"I would like to acknowledge the outstanding work of our staff from both the Criminal Investigation Branch in Counties Manukau, where the original complaint was received, and the team in Lower Hutt who located the alleged offender today."
The man is due to appear in the Hutt Valley District Court on May 13, where he will face a charge of threatening to kill.
As the matter was now before the courts, there would be no further comment, police said.
Brown, who is the National Party spokesman for police, had been critical of Davidson's visit to the Waikato Mongrel Mob gathering, calling it an insult to victims of crime by gang members.
A day after Davidson's visit, he said he received three threats from what appeared to be a Mongrel Mob member - though from a different chapter.
"A Minister of the Crown going to their gang pad not only gives them credibility, but emboldens them in terms of what they're trying to do in our community. I find that absolutely shocking," Brown said on Tuesday.
Davidson told reporters on Tuesday her visit to the Mongrel Mob was about engagement with whānau-led solutions, "and that includes all whānau".
"It's vital we talk to a range of communities and I was happy to accept their invitation."
Waikato Mongrel Mob president Sonny Fatupaito said in a statement the death threats were wrong and should not be tolerated "by anyone, especially by people like us".
"I stand with him [Brown], as we all deserve to support and protect our families, no matter where we come from or the seemingly deep chasm separating us, which probably will continue."
Brown has previously clashed with the Waikato Mongrel Mob, most recently at a parliamentary select committee in March.
"When are your members going to hand in their firearms and stop selling meth, which destroys lives in our community?" he asked the chapter's public relations liaison Louise Hutchinson.
Hutchinson responded by telling Brown to come to the Waikato to see for himself, adding that Fatu didn't have any guns.
Brown: "Twenty-nine members were arrested last year with illegal firearms - Waikato Mongrel Mob."
Hutchinson: "That was not the Mongrel Mob kingdom. There's different chapters, Simeon."