The man, identified as Tony Pettway, 32, was arrested inside the Trump event and charged with the misdemeanor before being released, the Tucson Police Department said.
The incident began when an anti-Trump protester -- wearing an American flag shirt and carrying a sign that read "Trump is Bad for America" -- was being escorted out by law enforcement at the Republican presidential hopeful's rally Saturday.
Pettway, who was also in the crowd, then allegedly reached over, grabbed the sign out of the protester's hand and punched and kicked him in an incident that was caught on video.
Pettway was then placed in handcuffs and escorted out by law enforcement, as well. No officers were injured, police said.
Pettway could not be immediately reached for comment.
Police said Pettway's actions were captured on video by several witnesses.
Rally attendee Alex Slattery, a University of Arizona student, captured the incident on video and tweeted it.
Besides Pettway, Tucson police said a woman, Linda Rothman, 67, was arrested for assault no injury at the event before being released.
Police said it was unknown if Rothman was captured on video at the event. Rothman could not be immediately reached for comment.
Trump addressed the removal of the hood-wearing protester, but erroneously identified her as male.
"There's a disgusting guy, puts on a Ku Klux Klan hat on, he thinks he is cute -- he's a disgusting guy," Trump told the crowd, who overwhelmingly booed in agreement. "These are not good people, folks. They're throwing the flag all over the place... And they're not really protesters, they're agitators. And if [Maricopa County] Sheriff Joe [Arpaio] was here, they'd be in jail already. I want to tell you that. They'd be in jail a long time ago."
Protesters were escorted out of the arena before Trump took the stage, and during the rally, as well. Protesters also blocked the front entrance of the convention center, attempting to make it difficult for attendees to enter.
Earlier in the day, Trump's rally in the Phoenix suburb of Fountain Hills was delayed after protesters blocked a highway leading to Fountain Park, the rally's venue.