Derbyshire Constabulary has received 57 reports of dog thefts since 2013, according to a Freedom of Information Act request.
Experts say pedigree dogs including Staffordshire Bull Terriers and toy breeds like Pugs are most targeted as they can be sold on in the UK or overseas.
Becky Thwaites, public affairs officer of the Blue Cross animal charity, said: "The effect of having your pet stolen can be absolutely devastating for owners - and we want the Government to do more to deal with this increasing problem
"Penalties need to be tougher for those committing these crimes to act as a deterrent to others. We also believe that police forces need to ensure they deal with these cases in a sensitive manner and highlight where owners can go for further support."
The Blue Cross receives more than 6,000 calls and emails a year from people who are dealing with losing a pet.
Tracie McGrory, pet bereavement support manager, said: "A pet is an integral part of so many families who are absolutely devastated if they are stolen. Not only are they missing their pet they are also desperately worried about what is happening to them."
A Ministry of Justice spokesman said: "We are aware of the distress the disappearance of a pet can cause, especially if there are suspicions it has been stolen.
"The maximum penalty for theft is seven years imprisonment and there are no plans to change this.
"The independent Sentencing Council recently issued revised guidelines for dealing with theft which make clear courts should take into account the emotional distress."