Lance Corporal Jack Fitzgibbon suffered critical head injuries at the RAAF base in Richmond, north west of Sydney, on Wednesday night, when it is understood his parachute failed to deploy properly.

In a statement, Mr Fitzgibbon said serving in the special forces was his son's "dream job".

"We take some comfort from the fact that he died serving his nation in a uniform of the ADF," he said.

"Jack was a dedicated, highly skilled, and courageous soldier. He was an experienced parachutist.

"Our lives will never be the same without Jack, but we will always remain proud of him and his many achievements."

It's understood he was taken to Sydney's Westmead Hospital in a serious condition after he was injured during what defence has described as a routine training activity at the base.

"First aid was rendered at the scene and the member was taken to hospital by NSW Ambulance," the department said.

"Defence's priority remains with the member, their family and unit at this time."

Defence said it was investigating the cause of the accident, and the army had temporarily paused all parachute training in the meantime.

Members of the Second Commando Regiment have ceased training and have mustered at Holsworthy barracks to process the news.

Acting Special Operations Commander Australia Brigadier James Kidd said Lance Corporal Jack Fitzgibbon was a much-loved and respected soldier within the Second Commando Regiment, which is part of the Special Operations Command within the army.

"Jack was loved for his courage and known for his sense of humour and his service to the country," Brigadier Kidd said.

"Jack had served his country on operations abroad and also closer to home, serving his country and local communities as part of natural disaster responses.

"Defence has initiated a formal investigation into this incident as we seek to learn how we can strengthen our processes, but we acknowledge military training is inherently risky and we remain committed to constantly training at the highest standards to achieve the level of excellence we know our nation demands of us."

He said defence will be gathering around Lance Corporal Fitzgibbon's unit and that same support will be extended to his family.

"The army is a joint team and we are comprised of many team members, and many, many families and the Fitzgibbon family is absolutely a part of that community," he said.

Brigadier Kidd said it was too early to speculate about what went wrong.

"It was part of a routine military training exercise that was conducted around the Royal Australian Air Force base in Richmond," he said.

"We train parachuting exercises and operations with regularity.

"I am a special forces qualified parachutist, I know first-hand how difficult particular military skill is and we demand our paratroopers to reach the highest standard."

Joel Fitzgibbon served as the minister for defence from 2007 to 2009, and retired before the 2022 general elections.

Prime Minister Anthony Albanese said in a statement that his thoughts are with Mr Fitzgibbon and his family.

"The extraordinary men and women who volunteer to serve in the Australian Defence Force do our nation proud every day," he said.

"Every death in the service of Australia carries the heavy weight of loss and sadness. The tragedy of a life cruelly cut short.

"This tragic accident is a harsh reminder that there are no easy days for those who defend our nation."

Mr Albanese shared his gratitude to every Australian who serves.

"Today the burden of grief falls on a dear friend to so many in the Labor family," he said.

"Our hearts are filled with sorrow for Jack, and his loving family - Joel, Dianne and his sisters - who are now holding on to his precious memory.

"We think also of all who served with Jack and are now coming to terms with the loss of their friend and mate.

"May Jack rest in peace."