Police say the cat was in the front yard of its home on Jersey Road at Matraville last Thursday afternoon when it was mauled by the dog.
They say the pitbull-Staffordshire terrier cross was with its owner but was unrestrained.
A number of witnesses called police and a 32-year-old Matraville man was later arrested.
He has been charged with four offences under the Companion Animals Act, including being in charge of a dangerous uncontrolled dog in a public place.
Police say they are seeking to have the dog put down.
They say it was already subject to restricted dog rules which mean it should have been muzzled and on a leash.