Nicholas Ollier, of Victoria Road in Northwich, came home from playgroup last Friday to find Buns and his hutch missing from the back garden.
Mum Anita Ditchfield, 34, said: "How can someone take Buns who's so important to a little boy?
"Nicholas was wandering round the garden kicking things because he was so upset. I imagine they've taken him to keep rather than sell on. I just hope he's being looked after."
Buns is a three-year-old brown Norwegian rabbit and is rather special because he only has three feet.
"He had an operation on his back foot just before last Christmas - we didn't know whether he was going to survive," added Anita.
Nicholas, his 20-month-old sister Charlotte, Anita and dad Kevin are appealing to anyone who has information about Buns. If you can help ring Northwich police on 01606 48000.
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