A window has been smashed at the constituency office of Labour leadership challenger Angela Eagle.
The building in Manor Road, Wallasey, was targeted between 17:00 BST on Monday and 09:00 BST.
No-one was thought to be at the property at the time. Merseyside Police is investigating.
Labour leader Jeremy Corbyn said it was "extremely concerning that Angela Eagle has been the victim of a threatening act."
Ms Eagle announced her intention to challenge Mr Corbyn after resigning from the shadow cabinet.
Mr Corbyn said other MPs "are receiving abuse and threats".
He said: "As someone who has also received death threats this week and previously, I am calling on all Labour Party members and supporters to act with calm and treat each other with respect and dignity, even where there is disagreement.
"I utterly condemn any violence or threats, which undermine the democracy within our party and have no place in our politics."
Liscard Councillor Bernie Mooney said staff came into the office on Tuesday morning and "found a brick had been put through the window".
She said the manager found glass "up and down the stairs".
It was the first physical attack on the building, but she said Ms Eagle had been subjected to "hundreds of vile, horrid emails and messages on the phone".
She described her as "a very popular MP in Wallasey" and people in the area are "absolutely mortified" by the incident.
Another member of staff who had spoken to Ms Eagle was told by the MP she was "disgusted" by what had happened and "worried for her staff", she added.
Merseyside Police and Crime Commissioner Jane Kennedy has visited the constituency office to speak to staff following the brick attack, describing those who did it as "cowards".
She said: "It is an absolutely disgraceful situation that you cannot take part in a democracy without having this kind of threat.
"The violence of it, the vile nature of the abuse that is being given to Angela Eagle and to the other members of her staff and to those who support her is completely unacceptable."