Without the treatment, baby Kaan has been given between four and six months to live.
"He has very low phosphate, which means he has extremely weak bones that, without treatment, will not be able to handle growing or supporting his body as he grows himself - this is fatal," Roberts wrote.
"He is currently in Starship Hospital, where they are desperately trying to bring his calcium levels down, but this is just a temporary fix."
Roberts said the diagnosis had been "extremely hard" on her and Kaan's three other siblings.
"It will be a hard road ahead but I will not stop fighting to get my little boy the chance at life he so deserves!
"It has broken my heart to hear that I may not be able to afford to keep my child alive, but he is strong and we won't give up on him.
"Any and all support would be so gratefully appreciated by myself and our entire family," the page reads.
Roberts said all funds will go primarily towards funding Kaan's treatments, as well as travel to and from Starship and helping to support his parents and siblings while they fight for his life.
The Givealittle page, set up on Saturday, has currently raised just under $2000.
• Go to Please help baby Kaan- infantile hypophosphatasia to donate.
Infantile Hypophosphatasia:
• About 90 cases have been reported globally to date.
• The most severe forms of the disorder tend to occur before birth and in early infancy.
• Hypophosphatasia weakens and softens the bones, causing skeletal abnormalities similar to another childhood bone disorder called rickets.
• Affected infants are born with short limbs, an abnormally shaped chest, and soft skull bones. Additional complications in infancy include poor feeding and a failure to gain weight, respiratory problems, and high levels of calcium in the blood (hypercalcemia), which can lead to recurrent vomiting and kidney problems.
• Asfotase alfa is a drug used in the treatment of patients with infantile hypophosphatasia. It is a bone-targeted enzyme replacement therapy designed to address the underlying cause of hypophosphatasia.