0715 GMT February 20, 2019
Harri Stickler, from Aberdare in Wales, was suddenly diagnosed with a rare form of leukemia just before Christmas and has only a 20-30 percent chance of survival, BBC reported.
Since then, he has been receiving weekly chemotherapy in hospital.
His mother Bethan said, "I went to the doctor with a scratch on his eye and he came out with cancer, how can that happen?"
The blood cancer charity Anthony Nolan is helping the family by trying to find a donor match on its register and appealing for more people to come forward.
The GP had suspected possible meningitis and called an ambulance to take Harri straight to Prince Charles Hospital in Merthyr.
He was then diagnosed with acute lymphoblastic leukemia and transferred to the University Hospital of Wales in Cardiff.
His grandmother Anne Jenson said, "I saw Harri a couple of days before he was diagnosed and he didn't seem ill at all, so the news came as such a shock, it's just awful.
"He was in hospital over Christmas so as a family we didn't celebrate at all."
The baby's chemotherapy means he has a high risk of infection so only his parents can touch him.
"This is so hard for the rest of the family as we just want to hold him," said his grandmother.
"If you could have seen him at home he was so happy, he didn't seem ill. He's still happy now but he is ill and he needs a donor."
Only about 25 percent of matching stem cell donors can be found within families, so the register compiled by Anthony Nolan relies on strangers.
Donating stem cells means a short outpatient procedure similar to giving blood.
But the charity said the register is particularly short of younger men between 16 and 30.
"They provide more than 50 percent of all stem cell donations but make up just 18 percent of our register," said the charity's Wales development manager, Karen Archer.
Harri's mother added, "They have only given him a 20-30 percent chance of living until he is five. So it's really low but fingers crossed that we can do it.
"Even if joining the Anthony Nolan register doesn't help Harri, it will help someone else."