The horrific discovery in Chorley is said to have left the householder traumatised.
Officers were called to the property in the Great Meadow area of the town earlier today.
They found the head of a dog, believed to be a terrier, on the door handle.
“This was extremely distressing for the occupant who found the dog,” said a police spokesman.
“At this time, we have no idea why this has happened.
“If you have any information or are missing a dog, which is described, possibly as a terrier then please get in touch with PC Chris Hilton on 101 quoting log LC-20180520-0514.
“Alternative you can email [email protected] or contact CrimeStoppers anonymously.”
News of the gruesome find prompted scores of people to express their shock and disgust on social media.
One said: “How could enyone do such a cruel, sadistic thing?” Another wrote: “That’s horrific. Who the hell does something like that?”