Abraham Contreras said he found the animal Thursday morning when he arrived for work at the Baldwin Park Animal Care Center, KTLA-TV, Los Angeles, reported Friday.
"I thought it was odd that a cardboard box would be there, so I went to inspect it and I saw an animal moving in there," he said. "Upon further inspection, I saw something was taped around its face and its paws."
Officials said the cat, a 2-year-old that has been dubbed Amigo, was struggling to breathe with its airways blocked and likely would have soon died if it hadn't been discovered.
"The animal was gasping for air, barely able to breathe," said Department of Animal Care and Control Sgt. Luis Villegas.
"We are attempting to rehabilitate him by getting him into a different environment," Villegas said. "Hopefully, with a different environment, it will help him calm down."
Police said whoever bound the cat in duct tape could face animal cruelty charges if identified.