Giles Wooltorton was treated by medics outside Savoy Place off the Strand in central London after the incident.
Video footage shows BBC political editor Laura Kuenssberg crouching down next to him as he explained what had happened.
Channel 4 journalist Matt Spencer, who was also outside the building, tweeted: “This BBC cameraman has just had his leg ran over by the car Jeremy Corbyn arrived in at Labour’s manifesto signing.
“Jeremy Corbyn was in the car as the tyre ran over this man’s foot. He’s receiving medical treatment – Corbyn’s gone inside.
“BBC Cameraman Giles is in good spirits, but pain. An ambulance is just arriving.”
Jeremy Corbyn has so far not commented on the incident.
It has not been the best day of campaigning for the Labour leader, who was faced with embarrassment this morning when a leaked version of the Labour party manifesto was published.
The 43-page document outlined radical plans for what Mr Corbyn would want to do if elected Prime Minister next month.