Staunch Brexiteer Ms Leadsom condemned the message as “despicable” and described its anonymous sender as a “coward”.
The Metropolitan Police confirmed it is investigating after four MPs received similar messages, which were all signed off from “the real 48 per cent”.
The “real 48 per cent” is an apparent reference to the number of people who voted Remain in the June 2016 EU referendum.
Senior minister Ms Leadsom, who campaigned for Leave, revealed she had been sent the death threat letter on Monday.
A constituent of Zac Goldsmith also received a similar letter last week. It is not clear who the other three MPs who received the notes are.
It warned: “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.”
According to Mr Goldsmith, the letter read: “If you attempt to take away part of someone’s identity. There are consequences.
“We have watched, you have stoked the fires of Brexit and led us to this moment.
“You can no longer be tolerated. We are coming for you. We are going to kill you.”
Met Police said at the time that they were looking into a “malicious communications allegation” after the Richmond MP said his constituent had received the threatening letter.
No arrests have been made.
A Metropolitan Police spokesman today said: “Police are aware of threatening letters sent to four Members of Parliament at the House of Commons.
“Two of the letters were reported to police on Friday February 9, and two on Monday February 12.
“The letters are being investigated by officers from the Parliamentary Liaison and Investigation Team within the Parliamentary and Diplomatic Protection Command.
“There has been no arrest at this stage. Enquiries are ongoing.”