Femi Oluwole said he fears for his safety when out campaigning because he is seen "as a significant threat to Brexit".
The pro-Remain campaigner said he was aware he could face "physical danger" as a result of his views on stopping Brexit.
"Do I know that there is a physical danger out there in terms of my safety? Yes, I'm aware of it," he told talkRADIO's Matthew Wright. "I have done the maths in my head."
"Given what happened with Jo Cox in 2016, given the fact that I'm now seen as a significant threat to Brexit, given that the sorts of people who did what they did to Jo Cox find me offensive because of the colour of my skin, there is a significant physical threat towards me."
His appearance on talkRADIO followed a race row, which erupted after Brexit Party campaigner Andy Wigmore tweeted that Mr Oluwole resembled the Labour MP Diane Abbott.
Mr Wigmore, who was Leave.EU's communications director, posted: "Have you eaten Diane Abbott Femi? You sound like her, you have a grasp of numbers second only to her AND you even look like her, although you have much more of glowing complexion.”
Mr Oluwole added: "The only thing that I have physically in terms of appearance with Diane Abbott is the colour of my skin.
"If he is saying that I look like Diane Abbott purely because of the colour of my skin, he is implying that all black people look alike."
However, Twitter ruled that Mr Wigmore's tweet did not violate any rules.
But Mr Oluwole said it was for "society" to decide what was racist, not Twitter.
"It is racist, and it's on us as a society rather than Twitter as an organisation to call that out."