Currently, she was in the High Dependency Unit at North Shore Hospital where the medical staff were trying to resolve blood clots in her lungs.
While Mrs Hyndman was also awaiting tests to see just what type of cancer it was, she said: "being realistic, the life expectancy isn't measured in years."
On Facebook, many have posted their sympathy for the new mother and encouraged others to donate.
Injured wakeboarder Brad Smeele encouraged people to pay it forward.
"When my injury happened, my friends and family set up a give-a-little page to help raise money for my recovery. I had an overwhelming amount of support that I am eternally grateful for.
"Rebecca Hyndman just recently became a mother to a healthy baby boy ... please help her and her family by donating what you can."
UK-based Rob Vivian expressed his sympathy for his "family while I lived in New Zealand".
"I am indebted to them for their generosity. They are all awesome and this is such sad and tragic news."
The friend who set up the Givealittle page, Anna Seccombe, thanked those who had donated towards the family.
"Rebecca is such a special soul and this is just so incredibly sad. She will leave a massive hole in our lives. I'm so grateful to people who are helping bring people to the Givealittle page so we can give Bex some comfort and Jeff a financial buffer."
Mrs Hyndman also expressed her gratitude to those who donated.
"For the first time in my life I'm basically speechless. But tonight I've got one message and that is one of complete, unreserved and absolutely overwhelmingly grateful thanks.
"On a personal level, you'll never know the comfort level this has given me; I close my eyes tonight much easier and will continue to dream good dreams for my little family. Thank you isn't enough, but for now it'll just have to do.