The front-runner in the race to be the Republicans' US presidential candidate addressed supporters in Fountain Hills.
Some 50 protesters caused traffic jams as they held up posters with slogans such as "Dump Trump".
The billionaire's rallies have been marred by a series of recent incidents. A meeting in Chicago a week ago was cancelled after protests.
Hundreds of demonstrators had gathered at the University of Illinois and fighting broke out between supporters and protesters in the auditorium where Mr Trump was due to speak.
Criticism over violent Trump rallies
What Trump says about protesters at his rallies
Why are Americans so angry?
In the latest disturbance, protesters marched down the highway leading to Fountain Hills. Police made several arrests before the demonstrators dispersed.
Some, heavily outnumbered by Trump supporters, made their way to the edge of the rally venue in Fountain Park.
Speaking later at a rally in Tucson, Mr Trump described the protesters as "disgraceful" and said they were "representing [Democratic front-runner] Hillary Clinton".
"They arrested three people and everybody else left... They left!" Mr Trump told a cheering audience.
"I love our police, but we should do a little bit more of that, you would have a lot less protesters, you would have a lot less agitators."
Demonstrations also broke out there and the police had to escort out a number of people.
In Mr Trump's home city of New York, several hundred protesters gathered outside Trump Tower in Manhattan.
Some chanted slogans accusing him of racism, sexism and being anti-gay. The gathering included immigrants' rights activists and socialists.
Several protesters carrying "Vote Trump" placards were also present, explaining that they wanted to demonstrate their right to support Mr Trump.
On 12 March, a man tried to rush Mr Trump as he spoke on stage in Ohio but was prevented from doing so by Secret Service agents.
A Trump supporter was also charged with assault after multiple videos showed him punching a protester at a campaign rally in North Carolina.
Mr Trump has been accused of creating tension through divisive rhetoric, but he denies using hate speech or playing any part in fostering division.
The Arizona rally was the Republican hopeful's second visit to the state in three months. A primary takes place there on 22 March.
The winner in Arizona takes all 58 delegates at stake. The billionaire leads the polls in the state.
Mr Trump and Mrs Clinton strengthened their leads in a series of primaries last Tuesday.

Titled "Albert Finney was never a member", it debunks myths while also celebrating past events at the venue.
Project manager Leslie Holmes said: "Our plaques are a bluey green, to be a bit different from the official English Heritage scheme."
It is being held in conjunction with the Manchester International Festival.
Mr Holmes said: "Whenever I go to London, I'm always amazed by how many blue plaques there are about the lives of the rich and famous, but hardly any in Salford, so I thought it would be good to change this - even for the weekend - and put 20 plaques here at Salford Lads Club."
He said the exhibition's title was "a humorous way of putting the record straight" on a myth that Salford-born actor Finney, who appeared in Skyfall and The Bourne Ultimatum, was a member when he was a boy.
The plaques, designed by the artist Amber Sanchez, will be on display at the venue until Sunday afternoon.
Demonstrators blocked a highway in Arizona as Donald Trump prepared to stage a rally near Phoenix.
[NEXT_CONCEPT]
A display of spoof blue plaques on celebrities' links with Salford Lads Club, which famously appeared on an album by The Smiths, has gone on show.