Barnsley South Neighbourhood Policing Team reported there has been a number of incidents where domestic cats have been found injured, particularly in the Fitzwilliam Street area.
Officers say they do not know exactly how the injuries came about, but admitted they cannot rule out foul play.
A spokesperson added: “We are asking residents to remain vigilant and report any such injuries to SYP and the RSPCA.
“If any person observes any offences taking place we request that this is reported to us via 999.
“Enquiries are ongoing into these incidents - should anyone have any information that may assist please call 101.
“You do not have to leave your name or number and all calls will be treated in the strictest confidence.”