According to a BBC reporter covering the rally, the attack happened after President Trump had launched heavy criticism towards the news media.
A BBC spokeswoman said Mr Skeans was "violently pushed and shoved by a member of the crowd" as he covered the rally.
President Trump has repeatedly claimed journalists are "the enemy of the people" and reporters of "fake news" since taking office in 2016.
The BBC's Washington Correspondent, Gary O'Donoghue, tweeted the shocking video on Twitter.
The footage captured from Skeans' camera shows the shot focused on Trump before jolting away as he is pushed by a man.
Skeans recovered to film a man in a red "Make America Great Again" cap being restrained and shouting: "Fuck the media".More news: Kamala Harris: I’ve Smoked Weed and ‘I Did Inhale’
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During his speech on Monday, Mr Trump told the crowds inside El Paso County Coliseum that 69,000 people had signed up to attend. Fortunately our cameraman is fine, he is made of stern stuff, ' O'Donoghue told the Today programme.
He added: "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", he added. And they made clear that Mr Trump's long-promised border wall is sure to play an outsized role in the presidential race, as both sides use it to try to rally their supporters and highlight their contrasting approaches.
Last year, United Nations experts warned that Mr Trump's "strategic" rhetoric against the media "increases the risk of journalists being targeted with violence".
"The crowd had been whipped up into a frenzy against the media by Trump and other speakers all night".
There were no reports of injuries following the attack and the BBC reporter tweeted that her cameraman was fine. According to BBC, a Trump campaign official suggested that the man causing the violence was drunk.