The tweet was sent to Dawson from Tanya Heti, who has been suspended from her mentoring job at Melbourne's Monash after Dawson reported her abusive tweets to the university.
Dawson, who hosts Australia's Next Top Model, identified Heti from a business card she had posted on Twitter. She challenged her after Heti attacked Bernadette Casey, who had defended Dawson following an earlier abusive tweet which also referenced suicide, News Limited reported.
When Casey told Heti she had lost her partner to suicide Heti responded "if I was your fiance I'd hang myself too #gohangyourself."
Heti, also from New Zealand, would not comment to News Limited on the tweets, but Monash University said in a statement it "does not condone or endorse the comments made by Tanya Heti in relation to her Twitter exchange with Charlotte Dawson".
"The University has directed Ms Heti to take leave with pay and is in the process of investigating the matter at this time," university spokesperson Stacey Mair said.
Dawson is an ambassador for Community Brave, a project to eradicate online bullying, homophobia, transphobia and youth suicide.
However Dawson is no stranger to sending controversial tweets, and has been accused of bullying on social media herself.
In a News Limited live chat yesterday, several commenters also took issue with Dawson's tactic of "retweeting" abusive comments.
"I have never encouraged anyone to act, it's in my feed if they want to react," Dawson replied. "I respond with humour, especially with the really vitriolic material.
"They need to know their content will be retweeted. If they don't want to take responsibility for publishing bile against people then they need to take that responsibility.
"It's also great for showing people how abusive cowards dish out vitriol with no apparent consequence. People posting on a public forum are aware that content may be retweeted and commented on. It's a great thing."
Dawson said internet trolls "are often time rich and fairly angry or lonely people".
Earlier this month Dawson told the Herald on Sunday why she left New Zealand, saying her native country is "small, nasty and vindictive. It's a tiny, little village ... a tiny country at the end of the earth".
- By Paul Harper of Herald Online
