A 55-year-old man from Harrogate has been arrested in connection with social media messages sent to MEP Sajjad Karim.
The man was questioned by North Yorkshire Police on Friday.
He has been released on bail pending further inquiries, a force spokeswoman said.
Last week, Mr Karim, Conservative MEP for the North West of England, told the BBC that he had received threats.
The politician said: “Other than the type of conduct that I have had to face, there has been very direct threats made, which are now currently with the police, are being investigated and I anticipate that there are individuals who will be spoken to as a result of those threats.”
A North Yorkshire Police spokeswoman said: “A 55-year-old Harrogate man was arrested on Friday 17 June 2016 in connection with social media messages sent to an MEP.
“He has been released on bail pending further inquiries.”