Ron Skeans was filming a rally in Texas on Monday night when he was assaulted by one of the president’s supporters.
Washington correspondent Gary O’Donoghue said Mr Trump had “repeatedly goaded” the crowd and attacked the media beforehand.
The suspect, who appeared to be wearing a red “Make America Great Again” hat, got on to the reporters’ platform – giving the experienced cameraman a “very hard shove”.
Footage shows Mr Skeans losing control of the camera for about 10 seconds before his shot focuses on a swearing man who is being restrained.
In a statement, the BBC said on Tuesday: “Ron Skeans was violently pushed and shoved by a member of the crowd while covering a President Trump rally in Texas last night.
“The man was removed by security and Ron is fine.
“The president could see the incident and checked with us that all was okay. It is clearly unacceptable for any of our staff to be attacked for doing their job.”
Mr O’Donoghue shared footage of the incident on Twitter, writing: “This is the shameful moment when my cameraman Ron Skeans was attacked by @realDonaldTrump supporter in El Paso – after the President repeatedly goaded the crowd over supposed media bias.
“Happily Ron is fine #TrumpElPaso.”
Mr O’Donoghue told the Today programme that a goading of the crowds against the media is a “constant feature” of Trump rallies.
The correspondent, who is blind, said: “I have been spat at before, they hurl abuse at American colleagues in particular.”
His Twitter post is gaining traction on social media, with many users commenting on the incident.
One person said: “Absolutely horrific! The fault is on @realDonaldTrump himself *and* his supporters involved!”
Another wrote: “It must be like swimming in a shark tank.”
During the rally in El Paso, Mr Trump told crowds that 69,000 people had signed up to attend the event.
The president said: “The arena holds 8,000 and thank you fire department, they got in about 10 [thousand].
“But if you really want to see something, go outside. Tens of thousands of people are watching screens outside.”
A spokesman for the El Paso fire department has reportedly rejected Mr Trump’s claim and said 6,500 people were allowed inside the venue – the building’s capacity.