A 19-year-old rugby player remains in a critical condition in Wellington Hospital after suffering a brain injury in a tragic on-field accident.

The Wellington Football Club Colts grade player was placed in an induced coma and had brain surgery on Saturday night after the injury in a match that day at Ngati Toa Domain in Porirua.

The player's family said in a statement the injury was "a tragic accident".

"He was doing what he loved, enjoying the game he has played since he was 7 years old. What happened was nothing more than an accident," the family said.

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"Family and friends are with him at his bedside at Wellington Hospital and they want to express their thanks for the wonderful care he has received from the paramedics, rugby supporters at Ngati Toa Domain, and from the amazing staff at Wellington Hospital.

"They also express their gratitude for the love and incredible support they have received from friends and the Wellington rugby community."

Wellington Rugby chief executive Steve Rogers said It was unclear precisely what led to the head injury, but an inquiry was underway involving Wellington Rugby and NZ Rugby.

"Although no single incident has been identified as the cause of the player's injury, witnesses have reported the player was involved in a collision during the first half of the match," he said.

"There are no allegations of foul play.

"What we do know is the player was removed from the field late in the match after teammates noticed he was displaying worrying symptoms during a stoppage in play.

"Shortly after leaving the field his condition deteriorated rapidly and ambulance officers already at the ground attended to the player. He was taken to Wellington Hospital where he underwent brain surgery on Saturday night."

A hospital spokeswoman said on Tuesday that the player remained in a critical condition in the hospital's intensive care unit.

Club president and former broadcaster Keith Quinn told Fairfax Media he and rugby legend Murray Mexted visited the young man in hospital on Tuesday "to meet the family and pay our respects".

Rogers said Wellington Rugby was working with the Rugby Foundation and NZ Rugby to ensure that full support, including counselling, was available to all parties involved.

"The thoughts and prayers of the Wellington rugby community and the Wellington Club are with the player and his family," he said.

An Investigation by Herald journalist Dylan Cleaver found last year that many former rugby players were suffering from dementia after head injuries in their playing careers.

In March NZ Rugby unveiled a $7 million plan to tackle the issue, including asking referees to get players off the field if there was any chance that they had suffered a head injury.