She added: "I know that his spirit lives on through our conservation work and I hope together we can make him proud."
Bindi had already assured her social media followers that Australia Zoo - the Sunshine Coast attraction and conservation facility which is run by her family - is safe from the fires.
The conservationist also revealed she and her family have rescued and treated more than 90,000 animals affected by the fire.
She wrote: "With so many devastating fires within Australia, my heart breaks for the people and wildlife who have lost so much. I wanted to let you know that we are SAFE. There are no fires near us @AustraliaZoo or our conservation properties.
"Our Wildlife Hospital is busier than ever though, having officially treated over 90,000 patients. My parents dedicated our Australia Zoo Wildlife Hospital to my beautiful grandmother. We will continue to honour her by being Wildlife Warriors and saving as many lives as we can. (sic)"
Earlier this week it was reported that the animal death toll from the fires was estimated to have passed one billion. That includes deaths from related causes such as starvation and dehydration.