British lawmaker Yvette Cooper said she received the message on Tuesday, BBC reported.
A British Labour Party MP received a message via micro-blogging website Twitter which threatened the lives of her children and grandchildren.
Yvette Cooper, a former Cabinet minister and lawmaker for MP Normanton, Pontefract and Castleford, said she received the message on Tuesday, BBC reported.
The comment accused her of sending pro European Union (EU) "propaganda", adding "Please stop or I will kill your kids and grandkids".
The account from which the message was sent now appears to have been removed, police said.
The incident comes amid increased security for MPs following the death of Labour MP Jo Cox last week.
Ms Cox died after being shot and stabbed in an attack in Birstall near Leeds on June 16. A 52-year-old man has been charged with her murder.