The tragic incident has resonated with the public and a fundraising campaign has been set up.
The Givealittle website has already raised more than $17,420. The site says the fund has been set up to help support Asha while she grows up.
Mr Barr is survived by his wife Laura Barr and his infant daughter Asha.
A large number of donations have been posted on the site with some heartfelt messages being sent to Asha and Mrs Barr, including a donation and message from Peter and Trudy Hobson.
"Such a tragedy. Our thoughts to your wife, daughter and family. You were one of the good guys. Cheers Robbie for everything."
Kerrin Mato said: "I'm so sorry for your loss.
"Thoughts are with you and your beautiful daughter. I am a mother and it breaks my heart.
"Kia kaha and you raise your girl knowing that her daddy loves her.
"I am from Pukehou Hawke's Bay and this really hit home. Arohanui to you and your whanau."
Nicki and Simon Reisima posted Mr Barr's legacy would live on through his "beautiful girl".
"She will know how amazing her father was, and how much he loved her and her mum.
"It's truly a tragedy that she won't grow up with his physical presence, but he'll always be in her heart and will live through the stories of others, and will watch over her and her mamma. All our love xxx."
Mr Barr had only been working for Schaw Building Ltd for two weeks, business owner Marcus Schaw told Hawke's Bay Today the day after the tragedy.
"I've known him for years, I played rugby with him but he only started with us two weeks ago. He was as tough as buggery and very popular with his teammates and at work."
Central Rugby and Sports Club premier team manager Tony Lepelaars described the incident as a "freak accident".
He said Mr Barr tripped while holding a nail gun and it fired striking him in the shoulder area.
The builder realised what had happened and walked outside and sat on a trail and removed the nail.
Mr Lepelaars said Mr Barr was still in good spirits and even walked to the Lowe Corporation Helicopter which transported him to Hawke's Bay Hospital.
Mr Barr died the following morning. His case has been referred to the coroner.
The incident is currently being investigated by WorkSafe New Zealand.
If you would like to donate to Asha's appeal, visit: givealittle.co.nz/cause/AshaRose.