Byrne, the painter and creator of Tutti Frutti and the Slab Boys, lived in Nairn, near Elgin, for many years and his children are still based in the area.
The council, which is independent-Conservative run, voted to completely cut the arts grant, saving £62,000 for the rest of this year, and £94,000 in 2013/14.
Byrne said: "I think it is outrageous. The grant that is being cut is peanuts, it's tiny, so it doesn't make much sense to me. It sends a bad message about the area too, it does not encourage people to go there. Other councils will have a look at this and think they can get away with it. I am saddened because it's such a lovely part of the country."
Creative Scotland, the national arts funding body, said: "The value the arts can deliver for people and communities far outweighs the relatively small level of funding cut. However, we will continue to work with arts organisations in Moray."
Council leader Allan Wright said the arts cut reflected "what people said they were prepared to live without" after a period of consultation. He added: "The council's priorities must be care for the elderly, education and social services for the most vulnerable in our society."