Speaking on BBC's Today programme, Mr O'Donoghue claimed the incident was an "incredibly violent attack".
As the footage shows, Skeans was recording Trumps speech when the footage suddenly stumbles forwards as he is hit.
Ron Skeans was filming a rally in El Paso, Texas on Monday night when a man got onto the reporters' platform screaming "f*** the media" and shoved the camera into his colleague.
Montague tweeted: "Just attended my first Donald Trump rally where my colleague BBC cameraman Rob Skeans was attacked by a Trump supporter".
'The man was removed by security and Ron is fine.
As the camera appears to visibly bounce around for around 10 seconds, the screen then focuses on a man in a red "Make America Great Again" cap who is being restrained by another man in a black t-shirt. He added he had previously been "spat at" during a Trump rally.
BBC Washington correspondent Gary O'Donoghue said the attack was "incredibly violent" and "was a constant feature of these rallies - a goading of the crowds against the media".
Police in Miami release surveillance video of a possible abduction
Anyone with any information can call 911. 'He was running over here. "He hit her like 20 more times with the door". She was visibly distressed when the male figure dragged her out of the workshop and into the White Nissan Altima.
CNN's Jim Acosta has been heckled several times at Trump rallies with supporters of the United States president shouting "fake news" and "go home" behind him.
Trump had used his rally to encourage support for his proposed border wall with Mexico, which he claims will protect the U.S. from violent criminals, drugs and a "tremendous onslaught" of migrant caravans.
The BBC's Washington news editor, Eleanor Montague, said Trump had whipped the crowd "into a frenzy against the media" prior to the attack.
According to a BBC statement, this time Trump "could see the incident and checked with us that all was OK".
Trump has been openly hostile to the press throughout his presidency - accusing them of publishing false stories on him.
"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.
The sound of booing resounds throughout the El Paso County Coliseum as the attacker is drawn away.
Mitt Romney, a senator from Utah and former Republican presidential nominee, argued a year ago that Trump's tactics are detrimental to democracy.