The debating society had invited Mr Tyndall to speak in the debate on 17 May.
But following the nail bomb attacks on two areas with high ethnic minority populations in London, Thames Valley Police had told the Union the debate was "inappropriate".
'Extremist threat'
A spokesperson for the Oxford Union said: "This is not a victory for those who objected to the principle of extending an invitation to Mr Tyndall, rather it is a sad day for all those who believe that violence or the threat of violence has no part to play in modern society.
"Notwithstanding our continued and fundamental belief in freedom of speech, we must recognise that the safety of our members, guests and the local community is paramount.
"Thames Valley Police were unprepared to provide sufficient security to protect our premises and demanded that the Union pay for policing costs that the Union's limited resources cannot meet.
"If this debate were to go ahead, given the attitude of the police, the cost of implementing effective security and the threat from extremist organisations, there would be a worrying likelihood of opening the Pandora's Box of violent confrontation on the streets of Oxford, with a risk of injury and damage to property."
The invitation to Mr Tyndall had been made before the recent bomb attacks in Brixton and Brick Lane, the spokesman added.
Thames Valley Police Superintendent Wiz Bunce said in a statement that the Oxford Union had sought his views on whether the event should go ahead.
Tyndall 'an expert'
"My advice was that, in view of the increased apprehension in all sections of the community following the recent explosions in London, it may be inappropriate to proceed with this debate at this time.
"Foremost in my mind when formulating this advice was the safety of those debating the issue, those attending the event and the general public in Oxford." The debate was arranged during the Easter vacation in association with Oxford University's Student Union - a wholly separate body - as part of the student union's anti-racism week in May. It would have tackled the motion: "This house believes that racism is inevitable".
Mr Tyndall had been invited because he was, as a spokesman put it, "an expert in this field."
The spokesman said that a number of people had voiced their disquiet about the invitation, but there had not been any threats of trouble.
Also due to take part were the writer and broadcaster, Nick Fraser, and London School of Economics anthropologist Prof Peter Liozas.
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