“If UC Berkeley does not allow free speech and practices violence on innocent people with a different point of view – NO FEDERAL FUNDS?” Trump wrote on Twitter at 6.13am EST (1113 GMT).
He did not elaborate.
Representatives for the university, which has 38,000 students and a long history of activism, could not immediately be reached for comment outside of the school’s business hours.
Like other major US research universities, Berkeley depends on federal agencies for scientific grants and other support.
It was not immediately clear, however, what action Trump could take without authorisation from Congress, or without risking legal action.
Trump’s chief White House strategist, Steve Bannon, previously headed Breitbart News.
Hours before Breitbart’s Milo Yiannopoulos was to give a speech at Berkeley’s student union on Wednesday, hundreds of protesters clashed with police at the campus.
Demonstrators tossed metal barricades and rocks through the building’s windows and set a generator on fire near the entrance, footage from news outlets showed.
Police ordered the crowds to disperse, and the school was put on lockdown.
“We shut down the event,” one protester told CNN. “It was great. Mission accomplished.”
In a statement, the university blamed about 150 “masked agitators” for the violence during the otherwise mostly peaceful demonstration by about 1,500 people.
The school “is proud of its history and legacy as home of the free speech movement” in the 1960s, the statement said.
Many of the protesters voiced opposition to Trump, CNN reported.
The president’s executive orders and proposed policies, including his suspension of the US refugee programme and temporary ban on travelers from seven Muslim-majority countries, have triggered largely peaceful demonstrations by tens of thousands of people across the US.
Yiannopoulos, whose Twitter account was suspended last year after he was accused of participating in the online harassment of a black actor, told Fox News that he was rushed to safety by his security guards and police after protesters began throwing rocks.
“Obviously it’s a liberal campus so they hate any libertarians or conservatives who dare to express an opinion on their campuses,” he said. “They particularly don’t like me.”
The British journalist is a vocal supporter of Donald Trump – nicknaming the US president “Daddy” during his election campaign – and has become one of the faces of America’s “alt-right” movement.
Similar protests at the University of California at Davis last month also forced the cancellation of speeches by Yiannopoulos and former pharmaceutical executive Martin Shkreli.
The events at Davis and Berkeley were organised by conservative student groups.
A similar invitation to speak at UCLA was rescinded and Berkeley was to be the last stop of his tour.
More than 100 UC Berkeley faculty members had signed two letters sent last month to the school’s chancellor, urging him to cancel the event.
“Although we object strenuously to Yiannopoulos’s views – he advocates white supremacy, transphobia and misogyny – it is rather his harmful conduct to which we call attention in asking for the cancellation of this event,” read one of the letters.
They cited as one example an incident in December at the University of Milwaukee where Yiannopoulos – a gay crusader against “political correctness” – openly mocked a transgender student, displaying her name and photo on screen.