Stella Creasy, from the opposition Labour party, has received threats culminating in a tweet of a picture showing a masked man brandishing a knife while Caroline Criado-Perez received rape threats.
They are among a number of high-profile women recently targeted by so-called trolls.
The man being questioned by police, from Bristol in south-west England, is the third to be arrested since the allegations came to light two weeks ago.
"The man was arrested under anti-harassment legislation," police said.
Female journalists and a high-profile historian, Mary Beard, have all been targets of abusive and often sexually explicit Twitter messages.
Some users boycotted Twitter last weekend to raise awareness of the intimidation of other users in what has become known as "trolling".
Criado-Perez became a target after she successfully campaigned to have novelist Jane Austen featured on a banknote.
Twitter has faced calls to do more to prevent abuse. It has brought in additional staff to deal with the problem and taken steps to re-draft procedures for reporting abuse.
Source: AFP via I-Net Bridge
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