Mum, Alicia Necklen, said the granted wish was "awesome" for Max and the whole family.
"We try not to have him treated differently in terms of missing out on things but the reality is that he does because he can't do a lot of things other children do ... so it's a bit of a treat for him," she said.
The chemotherapy had weakened Max's immune system, meaning he was held back from swimming and other activities to preserve his health, Mrs Necklen said.
Going to see the Mary Poppins show would be "incredible" for Max, who loved singing and music.
Mrs Winton said the family would stay at the City Life Apartments in Auckland for three days next week, when they would attend the Mary Poppins Musical and visit Auckland Zoo.
This is the second wish the organisation has granted Max. In 2011, a fire engine laden with boxes of toys arrived at his Tauranga home. Make a Wish Foundation volunteer Pat Roser said eligible children were nominated by paediatricians and the board made decisions about granting wishes.