The message to Andrea Leadsom, Commons Leader said: “You have taken lives on our side. Now we will take lives on yours. We are coming for you.”
An aide passed the letter to the Metropolitan Police yesterday.
Several other prominent Leave campaigners and donors have received similar letters.
Each one was signed: “The real 48%” – thought to refer to the 48 per cent of the electorate that voted Remain in the 2016 referendum.
Mrs Leadsom, posted a photo of the letter on Twitter yesterday.
She wrote: “Pretty despicable whoever sent me this. We live in a democracy – death threats because you don’t agree? And unsigned? Coward.”
The full text of the letter read: “If you attempt to take away part of someone’s identity, there are consequences. We have watched as you have led us to the edge of the abyss. We will watch no longer.
“You have taken lives on our side. Now we will take lives on yours. We are coming for you.”