Police in riot gear fired smoke grenades into the crowd. Protesters also interrupted Mr Trump's speech at the rally in Albuquerque.
Mr 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.
'Still in diapers'
The protesters had gathered outside the Albuquerque Convention Center, with banners that read "Trump is Fascist" and "We've heard enough".
