Monroe successfully sued Hopkins over two tweets published in 2015, asking if Monroe had "scrawled on any [war] memorials recently".
This had suggested Monroe had either vandalised a war memorial or "condoned or approved" of it, the blogger said.
Hopkins told the BBC: "No comment."
Monroe told the programme Hopkins's tweets had left the blogger "absolutely horrified".
"My brother is an officer in RAF, my dad was a paratrooper in the Falklands," Monroe said.
"As part of the evidence [from the trial], I've got six A4 ring-binders of tweets I received - somebody telling me I should be shot in the head, put in a wheelchair - all sorts of abuse.
"It wasn't just in the aftermath in May [2015].
"It was ongoing, every time it came up.
"The stress was so awful, I ended up leaving my partner.
"My relationship broke down, I was about to get married. I fell apart as a person.
"Online abuse permeates into every aspect of everyday life.
"It was a life-changing series of events.
"I had a complete breakdown."
Monroe said that having won Â£24,000 damages, plus legal costs, in a libel action earlier this month, "I've got space to breathe and do my actual work".
"It's been almost two years of weekly legal meetings," Monroe said. "So it's a huge weight lifted.
"I hope it teaches people to be a bit nicer to each other."
The case arose after some Twitter users highlighted an anti-Conservative profanity daubed on a memorial to the women of World War Two during an anti-austerity demonstration.
In May 2015, Hopkins tweeted: "@MsJackMonroe scrawled on any memorials recently? Vandalised the memory of those who fought for your freedom. Grandma got any more medals?"
The judge presiding over the case, Mr Justice Warby, ruled that the tweet "meant that Ms Monroe condoned and approved of scrawling on war memorials, vandalising monuments commemorating those who fought for her freedom".
He found that a second tweet from Hopkins "meant that Ms Monroe condoned and approved of the fact that in the course of an anti-government protest there had been vandalisation by obscene graffiti of the women's war memorial in Whitehall, a monument to those who fought for her freedom".
The judge added: "These are meanings with a defamatory tendency, which were published to thousands."
Monroe said Hopkins had initially been asked to delete her tweet, but "she didn't respond to me being nice".
"She blocked me immediately instead of responding," Monroe said.
"So then I said, 'Make a donation and it goes away.'
"And she didn't respond to that. In the months that followed, I made several offers to her to make an apology [without receiving one]."
Monroe added: "I've got a lot of compassion for her actually.
"It can't be nice for the whole world to be waiting for your downfall.
"I said to my followers on Friday, 'Don't be abusive, don't be unkind to her.' It doesn't make anyone feel good.
"I don't support her in what she does, but no-one will get anywhere by name-calling."
Watch the Victoria Derbyshire programme on weekdays between 09:00 and 11:00 on BBC Two and the BBC News channel.
Jack Monroe "fell apart as a person" after defamatory tweets sent by Mail Online columnist Katie Hopkins, the food blogger has told the BBC's Victoria Derbyshire programme.