Alongside the video, he said: "This is the shameful moment when my cameraman Ron Skeans was attacked by Donald Trump supporter in El Paso - after the President repeatedly goaded the crowd over supposed media bias".
"BBC cameraman Ron Skeans was violently pushed and shoved by a member of the crowd", the broadcaster said in a statement.
As the footage shows, Skeans was recording Trumps speech when the footage suddenly stumbles forwards as he is hit.
The cameraman told the BBC that the "very hard shove" came out of nowhere.
The footage captured from Skeans' camera shows the shot focused on Trump before jolting away as he is pushed by a man.
Mr O'Donoghue said Mr Trump's 2020 election campaign, which he thinks has begun, will be as "hostile and ill-tempered and divisive as the one we saw last time".
A Trump spokesman for the rally suggested that the protester was drunk.
Skeans recovered to film a man in a red "Make America Great Again" cap being restrained and shouting: "Fuck the media".
This isn't the first time Trump supporters have become violent towards news crew at a Trump rally.
Gary O'Donoghue, BBC's Washington correspondent, who also was there, said that the man had jumped onto the media platform and tried to smash the BBC camera. "Fortunately our cameraman is fine, he is made of stern stuff", he told the Today programme.
"I have been spat at before, they hurl abuse at American colleagues in particular", he added.
Mitt Romney, a senator from Utah and former Republican presidential nominee, argued a year ago that Trump's tactics are detrimental to democracy.
Standing in a packed stadium under a giant American flag and banners saying "FINISH THE WALL", Mr Trump insisted that large portions of the project are already under construction and vowed to fulfill his 2016 campaign promise regardless of what happens in Congress.
"I'm very anxious that the hostility whipped up by Trump and some in conservative media will result in somebody getting hurt", tweeted Jim Acosta in response to the Florida incident.
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