West Mercia Police are asking for witnesses to come forward following the unusual theft in Cherrington, near Newport.
Officers also said this is the second hutch to be stolen in the area.
The hutch, which is worth about £100, was taken between Saturday afternoon and Sunday morning.
However, the rabbit was not taken by the thieves.
PC Lee Thomas, said: "This is the second rabbit hutch to be stolen in the village in just over a month.
"What's maybe more unusual about this, is that the rabbit living in the hutch was not stolen but left behind.
"The animal was found by its owner happily munching on grass in the field."
Anyone with information is asked to contact police on 101 quoting reference 323S 140216. Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org