The BBC crew were attending the president’s “Finish the Wall" rally in El Paso, Texas on Monday night when the “incredibly violent attack” occurred.
In the video, the camera can be seen focusing on Mr Trump’s speech when suddenly the camera is pushed down and jostled with.
Seconds later, a man in a Make America Great Again cap can be seen shouting as he is restrained by security.
Washington correspondent Gary O’Donoghue said that a supporter of Mr Trump got on to the reporters’ platform and pushed the camera into cameraman Ron Skeans , before continuing to push him.
Mr O’ Donoghue told the Today programme: “It was an incredibly violent attack. Fortunately our cameraman is fine, he is made of stern stuff.
“This is a constant feature of these rallies – a goading of the crowds against the media. I have been spat at before, they hurl abuse at American colleagues in particular.”
Eleanor Montague who shared the video on Twitter said “the crowd had been whipped up into a frenzy against the media by Trump and other speakers all night.”
Last October, a Trump fan was arrested after sending bombs to high-profile opponents of the president and media outlets Mr Trump had spoken out against.
Cesar Sayoc, 56, from Aventura, Florida was arrested by federal authorities in connection with a spate of bombs that targeted CNN and politicians including Barack Obama and Hillary Clinton.
When Mr Trump was asked if he planned to tone down the partisan rhetoric at rallies following the incidents. Mr Trump said: "I think i've been toned down."