Riot police fired smoke grenades into the crowd. Protesters also interrupted Donald Trump’s speech at the rally in Albuquerque.
Donald Trump, the presumptive Republican presidential nominee, wants a wall to be built along the border with Mexico.
New Mexico is the most Hispanic state in the US.
The protesters had gathered outside the Albuquerque Convention Center, with banners that read “Trump is Fascist” and “We’ve heard enough”.
According to the Albuquerque Journal, as the rally got under way, the crowd grew angry – throwing stones at police and trying to set fire to Trump T-shirts they had stolen from a seller.
In a series of tweets, Albuquerque police said bottles and rocks had been thrown at officers and police horses, and damage to a Convention Center window may have been caused by a pellet gun.
Speaking to a crowd of 4,000 people, Donald Trump 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, the Republican candidate said: “Go home to mommy.”
Albuquerque is the first stop of Donald Trump’s tour of New Mexico.
Republican Governor Susana Martinez has been critical of Donald Trump’s attacks on immigrants and has not yet said if she will support his candidacy for the presidential election.
Susana Martinez and other senior members of the local Republican party stayed away from Tuesday’s rally.
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