The traps were discovered on waste land near to St John Fisher Catholic High School, in Park Lane, Peterborough, yesterday.
When the trap was opened, the cat ran away, and the full extent of the injuries it suffered are unknown.
Wildlife officer Pc Paul Carter said: “The use of animal traps is illegal unless they are used on private land as part of a pest control regime.
“There is no reason for these traps to have been placed in this area, and it is a wholly irresponsible thing for somebody to do.
“These particular traps are also illegal in their construction, as they have no stop catch to prevent the animal inside from being crushed to death once they are caught inside it.”
Anyone with information about the traps should call Pc Paul Carter at Sawtry police station on 0345 456 4564 or Crimestoppers, anonymously, on 0800 555 111.