Protesters threw burning T-shirts and plastic bottles at police outside the rally at a convention centre in Albuquerque.
Demonstrators held banners that read "Trump is Fascist" and "We've heard enough", and some waved a Mexican flag.
Police responded by firing pepper spray and smoke grenades at the crowd.
Protesters also interrupted Mr Trump's speech at the rally.
New Mexico is the most Hispanic state in the US, and Mr Trump has angered many with his comments on illegal immigration and his plan to build a border wall with Mexico.
The protest had begun peacefully outside the Albuquerque Convention Center a few hours before the rally began.
Tensions rose as Trump supporters began to arrive at the centre, the Albuquerque Journal reports. Both sides started trading abuse, including racial insults, and protesters threw water and water bottles.
As the number of protesters swelled to more than 600, the demonstration turned violent.
Albuquerque police said bottles and rocks were thrown at officers and police horses, and several were injured. They were seen responding by firing pepper spray and smoke grenades into the crowd.
Mr Trump, speaking to a crowd of 4,000 people, was typically robust in his response to the protesters.
"How old is this kid?" he asked of one that disrupted the rally, adding: "Still wearing diapers."
To others, he said: "Go home to mommy."
University student Karla Molinar told the Associated Press she took part in disrupting his speech because she felt Mr Trump was attacking members of her family who were living in the country illegally. She said she believed he is using them as scapegoats for the nation's problems.
This is not the first time violence has broken out at Mr Trump's rallies. He cancelled a gathering in Chicago in March after clashes between his supporters and opponents.
Albuquerque is the first stop of Mr Trump's tour of New Mexico, and his rally came on the same day he easily won the Republican presidential primary in Washington state.
His opponents have dropped out of the race, and he is now just a few votes short of securing the 1,237 delegates needed to officially become the Republican candidate for November's presidential election.
New Mexico's Republican Governor Susana Martinez has been critical of Mr Trump's attacks on immigrants and has not yet said if she will support his candidacy for the election.
She and other senior members of the local Republican party stayed away from Tuesday's rally.