Mr Dunne arrived at Christchurch Hospital in a stable condition and is being treated for back injuries in the hospital's trauma unit.
Mr Dunne, originally from Liverpool in England runs Deepseed, a skydiving jumpsuit and equipment manufacturing company with his wife.
His brother Tony posted a message to him on Facebook.
"Bro, you go to some extremes to test your suits that's all I'll say! Glad to see you ok and hope to speak with you soon xxx big love from your big bro & Maeve and get well soon xx."
Skydive Abel Tasman director Stuart Bean said Mr Dunne was known to many of the people at the festival and news of his injuries had been met with sadness.
"We're a small community and we all know each other and we're very sorry to see he's been hurt."
Mr Bean said an investigation would be carried out into the incident and the festival would go ahead despite the accident.
"That's what he would have wanted."
Mr Bean said the accident was a sport skydiving accident and not part of the company's commercial operations.
Mr Dunne had packed his own main parachute for the jump.
New Zealand Parachute Industry Association spokesman Keith Gallaher said the association would be conducting an investigation into the accident, alongside Skydive Abel Tasman.
"We will look at the equipment and the processes related to the accident. Some of the equipment will go back to Germany to get the information out of it (the automatic activation device)."
Mr Gallaher said it looked like the reserve chute came out on time and when the electronic data was downloaded at the German manufacturers they would know the exact height at which it was deployed.
He said that with the information they had so far, it didn't appear the accident was caused by operator error.
"The original opening of the main parachute seemed to be normal and then when he's gone to release the brake for the steering lines - that's when the issue seemed to have occurred."
Mr Dunne was using a New Zealand air sports parachute which is smaller than standard parachutes and designed "to go a lot faster".
Mr Gallaher said Mr Dunne was known to everybody in the industry due its size and Mr Dunne's company.
"Accidents like this are not that common....over the last few years it's got a lot safer to go skydiving. It's fair to say a lot of people haven't seen an accident of this nature at all."
The Good Vibes festival is an annual event which has run for 11 years.
At this year's event skydivers are attempting various national records including the largest female formation and largest wingsuit formation.
