Northern Ireland Justice Secretary Naomi Long said a line had been crossed after a “mob” turned up at her home on Wednesday night.
Her husband, Belfast Alliance councilor Michael Long, said “about 40 people, some wearing masks, came to our house to protest.”
The protest is believed to be about housing sex offenders in residential areas.
In a social media post, Ms Long wrote: “This is bullying and intimidation. This is threatening and completely unacceptable.”
Police attended the incident and said they will now review the footage to “consider whether any potential offenses were committed.”
As well as his role as Stormont Justice Secretary, Long is also the leader of the Alliance Party.
In her post, she said she was open to discussing the issues, but added: “Showing up at my house as a mob, some wearing masks, is simply unacceptable.
“It is not participation or a legitimate protest to show up at my house, harass my neighbors, harass my family and put pressure on the police.”
Previous death threats
In an article on X, her husband said the police car “had to remain outside the house overnight in case of an attack.”
This is not the first time Alliance Party officials have complained of intimidation.
In 2012, the party came under attack from loyalists after it backed a proposal to display the union flag at Belfast City Hall only on certain days.
Ms. Long received death threats and it was later revealed that she was being treated for skin cancer at the same time.
However, Mr Long said: “No one had protested at our house in 25 years” before Wednesday night's incident.
First Minister Michelle O'Neill of Sinn Féin called it “absolutely disgusting”.
She added that “showing up at someone’s house is intimidation, not protest. This is never acceptable.”
Ulster Unionist leader Mike Nesbitt said he was “shocked and horrified” by the actions of the crowd outside the couple's home.
“We live in a democracy. There are acceptable ways to express your opposition. Intimidation is not one of them.”
Social Democratic and Labor Party leader Claire Hannah said the party expressed its “heartfelt solidarity” to the Longs after the “disgraceful scenes”.
“There will always be political differences, especially in a place with such a rich history, but showing up outside a politician’s house and trying to intimidate him is sinister and completely wrong,” she added.