Anna Soubry, the MP for Broxtowe in Nottinghamshire, was the apparent target of an online message which read: “someone jo cox Anna Sourby [sic] please.”
The politician responded to the message on social media, calling the Twitter user a “sad cowardly troll” and noting the differently spelled surname.
Nottinghamshire Police later confirmed they were investigating the incident.
Afterwards Ms Soubry tweeted: “Thank u everyone for much appreciated support. Voices of hope & tolerance will not be bullied off #Twitter or anywhere else.”
On Saturday the Metropolitan Police said a 25-year-old man was arrested at his home in Bethnal Green on “suspicion of sending malicious communications”.
A spokesman said the man was in custody in an east London police station. He has not been charged.
It comes after Jo Cox’s murderer, 43-year-old Thomas Mair, was jailed for life for shooting and stabbing the Labour MP for Batley and Spen outside her constituency office in Birstall, West Yorkshire, in June.
Conservative MP Ms Soubry was a Remain supporter in the EU referendum, as was Mrs Cox.