The BBC reported that the politician faced a significant amount of abuse, particularly on social media, but that it was only when a series of offensive tweets from one individual emerged that she began to fear for her safety.
Messages included references to Jo Cox, the MP who was murdered in 2016.
Following this, the windows to her Partick constituency office were smashed and covered in tomato ketchup, with Ms Monoghan saying that it was “obviously meant to look like blood”.
The situation continued to escalate when a death threat was made against her.
The SNP for Glasgow North West told the BBC: "It was phoned in and it contained enough details about my personal life, enough detail to cause the police to take it seriously.
"I got a call from my office manager, the police had contacted him to say there was what they considered to be a credible threat.”
She was in London at the time of the call and was advised not to return to Glasgow.
She continued: “Because of the personal nature of the threat and the personal details – I knew he knew where I lived, I knew he knew who my kids were – I just had to be there.
"That evening when we came back from the police station to the house, the police wouldn't let us into the house until the whole area had been searched.
"They spent the night outside the house and very early the next morning we left and went to a safe place."
Ms Monaghan puts a lot of the situation down to social media, saying that social media companies must take action to end misogynistic abuse.
She is calling for a change in harassment and abuse rules on social media sites, saying that they give people a platform to constantly target and abuse others anonymously with little in place to protect those on the receiving end.