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The incident happened as the Labour leader arrived at the Institution of Engineering and Technology in London for a party meeting to discuss the draft general election manifesto.
Mr Wooltorton was said to be in good spirits while waiting for an ambulance.
The BBC said they were focussing on "making sure he was ok".
In a statement the broadcaster said: "An experienced BBC cameraman has been injured while filming at the Labour Party manifesto meeting.
"He has been taken to hospital for assessment and treatment. At the moment the BBC are focussing on their duty of care, making sure that he is ok."