Owners of Mila, a Bedlington Terrier, found her cowering in a bush in their Halesowen back garden on Thursday evening.
Burglars beat the dog - leaving her with nerve damage - after breaking into the house, West Midlands Police said.
Homeowner Julie Green said she was "heartbroken" to find Mila wounded by burglars, who did not steal anything.
"Whoever is responsible is heartless," said Ms Green.
"She is the friendliest dog and would greet anyone. Even though she is poorly she has been trying to roll over and wag her tail."
Vets believe Mila has neurological nerve damage, preventing her from placing her front feet on the ground.
Ch Insp Phil Dolby said police are following several lines of inquiry.
He added: "This did not happen in the dead of night - there will be people around the Albrighton Road area who could have seen the offender or offenders responsible for the break-in."
More on this and other Black Country stories
An 18-month-old family dog is unable to walk after burglars repeatedly kicked it in the head, police said.