Mr Varadkar tweeted this afternoon evening: "I want to pay tribute to @hazechu for standing up to racism.
"Public figures & their families are sometimes subjected to abuse & bullying from opponents but worst is reserved for those from minority backgrounds. Sometimes overt.
"Usually covert. Too often ignored. Always wrong.
Yesterday, the Lord Mayor revealed how she now looks out the window every day to check if it is safe to leave her home with her three-year-old daughter.
It followed an incident when the Lord Mayor was confronted outside her home in the Mansion House by people holding placards and posters.
"I didn't think my life was in danger but it was deeply uncomfortable," Ms Chu said.
"They've been calling for my resignation since I spoke about the shooting of George Nkencho. A woman stopped me and stuck her hand out, touching my body, and said: '’pleased to meet you'.
"I said I couldn't shake her hand because of Covid, and then I realised someone was filming me.
"I kept thinking, 'just get back to the door', when two of her mates surrounded me on either side and started questioning why I was wearing a mask.
"I edged towards the door and when I got there one shouted: 'Hazel Chu, you're going to turn into a shapeshifting dragon someday and we're going to catch it on camera'. It was bizarre.
"The guards arrived and there were more people, around 30, and a lot of shouts and screaming."
Speaking on RTÉ's Today with Claire Byrne, Ms Chu said it was scenes like this that prompted her to check outside the window every day to check if it is safe to leave her home with her three-year-old daughter.
"If I am taking Alex to creche I do double check. Mainly because I worry. I feel a little embarrassed saying that, because it shouldn't be like that."
She revealed how the little girl has previously been called a "mongrel", but said she was "too young to understand".
"Now that she's a little older, I'm hoping there won't be any more issues directed at her, but there have been there been some online comments...[that] she should be deported back to China and aborted there".
"This is why it's really important that people actually do call it out and try to address these issues now because I don't want my three-year-old to grow up to realise we're back in the exact same place as we were 20 years ago,” she added.
She said she recognised some of those gathered outside her home yesterday as they had “provided very direct, more racist abuse at me, on other occasions”.
"You do have to have a reason why you're there protesting. It can't be just because that they don't like the look of me because I can't change that.
"The home versus office thing is a hard one for me, because my child lives with me.
"As a mother, I like all mothers, fear what will happen for their children. What irks me is, if you're going to come at me, make sure that you have a reason, apart from the colour of my skin.
"When you take possession of the public place yourself, anyone, you will get harassment or abuse that comes with the territory."
A female member of the protestors was arrested and later fined for breaching public health laws.
Yesterday, Social Democrats councillors on Dublin City Council added their names to a cross-party statement of solidarity with the Lord Mayor.
Cllr Mary Callaghan, Deputy Lord Mayor of Dublin, stated: “I would like to offer Lord Mayor Hazel Chu my strong and sincere support as she continues to face unacceptable racism and intimidation, not just online, but now outside her home.
"She is highly respected by Social Democrats city councillors and does great work for the people of Dublin, both in public and behind the scenes.”