Stapleton, who played 61 games for the Sharks, sustained the injury while playing for Boorowa in a game against West Wyalong on April 9.
The match was abandoned and the 32-year-old was transferred to Sydney's Royal North Shore hospital where he has begun rehabilitation.
Stapleton has an 18-month old son with partner Kate and the couple are expecting a second child in July.
A GoFundMe page set up on behalf of his family said that Stapleton had damaged his spinal cord at the C4 level of his cervical vertebrae.
"At this stage, the injury has left Nathan a quadriplegic, paralysed from the shoulders down," the page read.
"While the Stapleton family remain hopeful that Nathan will regain some movement, it has become clear that Nathan will require long term support and care.
"Anyone who knows Nathan can attest to his determination and incredible work ethic. He has demonstrated this through his success playing in the NRL.
"There is no doubt that Nathan will bring that same determination and commitment to his rehab and recovery."
Cronulla are attempting to raise funds for Stapleton by auctioning off the jerseys worn in their Thursday night win over Manly.
