The three springer spaniels were reported stolen from the farm at Thornholme near Burton Agnes earlier this month.
While two have been returned to their elderly owner, the third - who answers to the name Keedy - is yet to be located.
He is described as two years old and liver and white with one black paw.
Police believe he could be in Manchester, Wigan or Preston and are keen to return him to his owner, who they say is very distressed and worried.
He and the other two dogs are microchipped and were taken from an outside kennel between 11pm on Thursday, February 11 and 6am on Friday, February 12.
Anyone with information that might help with the investigation should call police on 101, quoting log 76 of February 12.
Humberside Police's Wildlife and Heritage Crime Officer Rich Fussey said: “We are aware of the fear of dog owners after a number of social media posts about dog thefts.
“We have not seen an increase in our area but would always ask for people to take some basic crime prevention measure to protect their own dogs.
“Report any suspicious activity to the police, if you see people checking out properties please call us to report your concerns.
“If your dog is kennelled outside please ensure these are secure and locked and install CCTV to monitor your property if at all possible.
“If you are out with your dog please keep your dog under full and proper control, in sight and avoid leaving your pet tied up in a public place and outside shops.
“We very much welcome the raised awareness of this type of incident and would ask owners to remain vigilant and report any concerns to us.”