Wallace played rugby league for New Zealand Secondary Schools and under-18s, and in 2017 penned a contract to play with the Gold Coast Titans under-20 side.
"Wallace spent that season with the Titans then joined the Burleigh Bears in the Intrust Super Cup," the NZRL said in a statement.
"Playing at halfback and being the youngest member of the squad, Wallace was one of the Akarana Falcons star performers in their National Premiership championship victory in 2016.
"That same year he was named Auckland Rugby League's College Player of the Year.
"Wallace is described as a 'lovely and cheeky' young man, who had a great sense of humour and a great bunch of friends."
Wallace won selection after a standout season with the Mt Albert Lions in Auckland's Fox Premier Rugby League Competition.
Rest in Peace Zae, a young talent that will be sorely missed. Our deepest condolences go out to Zae's whanau and friends.
Posted by New Zealand Kiwis on Saturday, June 1, 2019
A Givealittle created to support Wallace and his family last month has raised over $30,000 since its creation on May 1.
However, in an update yesterday the page said he had died surrounded by friends and family.
"Zae's fight is over and he has slipped away peacefully from us all today," it reads.
"Zae's family and close friends have been humbled by your support and love, and blessed with the realisation he has touched so many lives in his to short time with us.
"The last weeks have been a terrible time for us all, but you have all made it just a little bit easier."
The page said Wallace's health deteriorated after he became ill with influenza, which led to pneumonia and then the infection.
Warriors halfback Chanel Harris-Tevita told Wallace to "rest easy brother" on Facebook.
Northcote & Birkenhead Tigers Rugby League said they were extending their "heartfelt sympathy" to Wallace's extended family.
They said on Facebook the death of the young man was devastating and would provide further details when they became available.
The Gold Coast Titans also paid tribute.
"It is with heavy hearts that we pass on the news of ex [Gold Coast Titans] U-20s player, Zae Wallace's passing this morning," they said yesterday.
"Zae's family and close friends have been humbled by your support and love, and blessed with the realisation he has touched so many lives in his to short time with us."
Elsewhere, Counties Manukau Touch posted about Wallace's death.
"It is with heavy hearts that we share with you, Zae has lost his battle and passed away earlier today. He was just 20 years old," they wrote on Facebook yesterday.
"The young sportsman, who returned to Auckland this year following a stint with the Gold Coast Titans under-20 side, had been in an induced coma at Auckland Hospital.
"Zae was an amazing footy player, and well known throughout all codes in Auckland. Many of our Counties Touch Whanau were good friends with the young star."
Semi-professional rugby league club the Burleigh Bears, who Wallace played for formally, said his family are in their thoughts and prayers.
"It is with great sadness that we inform you of the passing of Bear #340 Zae Wallace," it said on Facebook.
"Zae was loved by all at the Burleigh Bears and while he will be missed won't be forgotten.
"The Club would like to offer its condolences to Zae's family and friends especially parents Rose and Wayne and siblings Kirsten, Vann and Leigh in these tough times."
It is with great sadness that we inform you of the passing of Bear #340 Zae Wallace.
Zae was loved by all at the...
Posted by Burleigh Bears on Saturday, June 1, 2019
Wallace had already been in hospital for four weeks when the Givealittle page was created at the start of last month.
"For those of you who know Zae you will know he is a very talented rugby league and rugby player," the page reads.
"He is a very strong athletic young man who has been in Australia playing league and has just recently returned to NZ to continue playing league with the Northcote Tigers.
"Unfortunately, Zae has only played one game with them before being struck down with a sudden illness."
Meanwhile, Westlake Boys' High School have taken to Twitter to pay tribute to their former student and rugby league captain.
"The Westlake community is deeply saddened with the loss of former student, Zae Wallace. Sending all our love to his family and friends," it posted.
In yesterday's Givealittle update, the donors were thanked for the support they offered and funds would go towards Wallace's funeral expenses.
"Zae's family and close friends have been humbled by your support and love, and blessed with the realisation he has touched so many lives in his to short time with us," it reads.
"The last weeks have been a terrible time for us all, but you have all made it just a little bit easier ... He will always be in our hearts."