A 52-year-old man has been arrested over threatening and abusive phone calls, emails and letters received by Labour deputy leader Angela Rayner.
He was arrested at an address in Halifax, West Yorkshire, on Wednesday morning, Greater Manchester Police said.
Detective Sergeant Christopher Dean said: "Abusive, threatening or bullying behaviour towards anyone is completely unacceptable and we will always do what we can to ensure those responsible are identified and held accountable for their behaviour.
"Although we have arrested one man our investigation remains very much ongoing and we will continue to pursue all available lines of enquiry to identify all those responsible."
Ms Rayner reported receiving the threatening contacts over a number of weeks.
A spokesperson for Ms Rayner said: "Angela and her staff have received a number of threatening, malicious and abusive communications in recent weeks.
"We are working with the police to ensure that the perpetrators of these crimes are brought to justice and Angela would like to thank the police for their work during these investigations.
"Abuse and threats of this nature don't just have an impact on Angela but also on her family, her children and her staff who are on the receiving end of these communications.
"Angela is currently on bereavement leave after losing a close loved one and she looks forward to being back at work as soon as possible."
The arrest was directly related to a number of abusive phone calls the MP for Ashton-under-Lyme received on 15 October and the individual has been bailed pending further inquiries.
It comes at a time of heightened focus on MPs' security and the abuse they receive in the wake of the killing of Sir David Amess.
The Conservative MP for Southend West was fatally stabbed in a suspected terror attack as he held a constituency surgery in Leigh-on-Sea, Essex earlier this month.