Austin has cerebral palsy. He suffers from periventricular leukomalacia (a brain injury), asymmetric spastic quadriplegia, developmental delay and has problems with his vision.
Surgery to relieve the spasticity of his limbs was not available in New Zealand but was available in the US.
Austin's mother Helen Manning said the can was nearly full, which meant there could have been between $150 to $300 inside.
"I honestly can't believe it.
"What gets me is, there is a photo of Austin sitting on the tin in his wheelchair.
"We are trying to fundraise, which can be so stressful, and somebody would do this."
Mrs Manning said the CCTV footage from Farmer Jones showed a woman assessing how heavy the tin was before placing it under her top and walking out of the store.
"I can't believe someone would do something like that, you have to feel sorry for them to stoop to that level.
"It's awful for the people who have donated to Austin already. People have been so generous and wonderful so far."
Mrs Manning said about $44,000 had been raised for Austin's cause.
Farmer Jones owner Tony Smith said the theft was low.
"You can't get any lower than this, especially when we are trying to raise money for a boy like Austin."
Senior Sergeant Shannon Clifford said the incident happened on December 2, at about 5pm.
Mr Clifford said police were investigating.
