Charlie Bigg-Wither, who runs the Green Shed recycling centre at Mugga Lane tip and is known for decorating the family's home with a metric tonne of Lego, said his 21-year-old daughter Alison is "totally shattered" over the likely theft.

His daughter's sculpture is one of three he had custom made for each of him children when they were young.

"I had three of them custom made and someone last night stole Alison's one and I don't normally get upset about this but she is quite disabled and has autism," he said.

Ms Bigg-Wither had gotten particularly attached to hers.

"She is upset, because she doesn't connect to many things and that was one thing she had connected to," Mr Bigg-Wither said.

He said he was surprised that it had been taken as the sculpture would be difficult to miss.

"They are solid wood so they weigh about 50 kilograms each, they have been turned by a wood turner," he said.

He said he had last seen the statue at 3pm on Thursday. Anyone with information is urged to contact the Green Shed.

"If you find it in someone's front room please ask them to bring it back," he said.

The house's position as a Canberra icon was revealed as locals reacted to news of the theft. Many said they enjoy driving past the house, and condemned the move as a low act.

"This house always brings a smile to my face and my kids love it too. I hope it is returned soon," one woman wrote on Facebook.

Others commiserated with the family. "As a parent of a child on the spectrum I can imagine what this has done to this young lady and her family. To the person who stole, please return it," another man wrote.