Ms Moore, who works as a duty manager at West Liquor Lincoln Centre branch, said she first became aware of the theft after seeing CCTV footage.
"I saw [the donation box] on Friday night and then by Saturday morning it was gone. It just made me feel sick knowing that someone would do that. There is a picture of my daughter and I and a poster so everyone knows what it's for and the fact they could just take it is sickening.
"It makes you wonder, 'What is it that you needed it for that is more important than this?'"
Ms Moore's best friend, Anika Stratton, said she was disgusted by the brazen theft.
"I just want to get that message to them about what exactly it was that they were stealing. It is just a horrible thing for someone to steal. It is something that is going towards saving another person's life," she said.
"I just couldn't believe that a human would find opportunity out of that."
Ms Stratton estimated the jar contained up to $1000.
A spokeswoman for the police said the matter had been reported to them and the case was with the Waitakere investigation support unit.
This is the second time Ms Moore, who is mother to 11-year-old Ayla, has had to battle the brain tumour, which was discovered when she was 16. It was removed in 2011, when she was 22, but doctors warned it could come back.
In 2015, she was told the tumour had returned, but this time it was inoperable because of its proximity to a nerve that affects movement and speech.
Ms Moore has so far raised $26,739 and was hoping to have enough funds gathered from donation boxes, her Givealittle page, Help Heather Fight, and other sources to start treatment next month. The drug is believed to cost around $8500 each time it is administered.
"[My doctor] wants me to have enough money so I can continue the treatment every three weeks. I am hoping, fingers crossed, to be able to start it in about a month."
How long she has to stay on the drug will be determined by her results.
Ms Moore has already been through a strenuous treatment regime of chemotherapy and radiation, with little success.
She is currently on steroids, which prevent her from having seizures and reduce pressure on her brain, but suffers horrible side effects as a result.
"It is mainly the weight gain. I have been on steroids for about nine months and have gained 40kg. I am only on 2mg at the moment but I was on 12mg and on that amount you can't sleep, you get hair growing in places you don't expect it to ever grow, I have had my leg go numb down one side."
When she stops taking the steroids she loses her ability to speak and move the right side of her body.
"I don't know what would happen if I can't get the treatment."
Can you help? Donations can be made at the Givealittle.