Officers from the Met Police e-Crime Unit (PCeU) are questioning the man over alleged threats made via email and social networking sites against Louise Mensch.
The 40-year-old MP for Corby and East Northamptonshire wrote on Twitter earlier that she had been emailed by “morons”, blaming hacking groups Anonymous or LulzSec.
She also said that online death threats had been made to her children.
The Culture, Media and Sport Committee member tweeted: “To those who sent it; get stuffed losers. I have contacted the police via the House of Commons and the email is with them now. I don’t bully easily, kids. Or in fact at all.
“Oh and I am posting it on Twitter because they threatened me to get off Twitter.”