Tish Coleman, 31, of the 6400 block of South Maryland Avenue, was charged with felony aggravated cruelty to an animal and misdemeanor domestic battery, said Chicago Police Department News Affairs Officer Laura Kubiak.
Coleman is expected to appear in court at midday on the felony charge.
Police said Coleman was in a fight inside an apartment at the Maryland Avenue address about 8:05 p.m. and was "wrestled outside," where the cat was.
Coleman "continued to make a disturbance" outside and when Coleman's cousin stepped out, she found the cat and blood on the stairs.
Police stopped Coleman about a block away based on a description they were given and found a Swiss pocket knife with blood on the blade in her purse.
The cat had puncture wounds on its right side.
It has a criminal history a mile long