The former Cabinet minister, whose husband is former Shadow Chancellor Ed Balls, received the sinister message on Tuesday from an account that accused her of sending pro-EU “propaganda” by email, adding: “Please stop or I will kill your kids and grandkids”.
Reposting the threatening tweet to her followers, Ms Cooper commented: “Got this today for speaking out for Remain ... This has to stop”.
It is understood the account was removed after the MP for Normanton, Pontefract and Castleford reported the tweet.
The 47 year-old mother-of-three told her followers: “Police & @Twitter on case. But this is for all of us. Time to stop the hatred.”
The incident comes amid an increase in security for MPs following the death of Ms Cooper’s Labour colleague and fellow Batley and Spen MP Jo Cox.
Meanwhile, a parliamentary watchdog has written to all MPs saying it will speed up the process for handing out security funding “as a matter of priority” in the wake of the killing of Jo Cox.
It comes after major concerns have been raised over the safety of politicians.
In a letter to MPs, Ruth Evans, the new chairwoman of the Independent Parliamentary Standards Authority (Ipsa) which awards security funding, wrote: “I had wanted to introduce myself as Ipsa’s new chair in different circumstances.
“But, following the appalling murder of Jo Cox MP last week, I am writing to assure you that I am keenly aware of your concerns that improved security is needed for you, your staff and your families.
“I know that many of you have also expressed concerns about Ipsa’s current approach to processing applications for security funding.
“I recognise that security is at the uppermost in your minds and, to that end, I have asked that we review and accelerate this process as a matter of priority, working in partnership with the police and the House of Commons security service.”
Mrs Cox died after being shot and stabbed in an attack in Birstall near Leeds on Thursday last week.
A man has been remanded in custody after being charged with her murder.