The offence occurred in the Bilton area between 11pm and midnight yesterday, police said.
Three 12-week-old female pugs were stolen.
A spokesman for North Yorkshire Police said: "As part of extensive enquiries to track down the offenders and safely recover the puppies, officers are urging people to come forward if they have possibly been offered female pug puppies for sale since Saturday evening."
Officers said that pictures of the dogs are not currently available, and did not give a street address for where the crime took place in their appeal.
One of the pugs is fawn (light brown) in colour, another has a black face with a pink smudge and an umbilical hernia, and the third is a distinctive silver colour with an umbilical hernia.
The offenders are possibly from the West Yorkshire area, officers said.
Anyone with information is asked to call 101, select option two, and ask for the Harrogate Serious Crime Team.
Or contact Crimestoppers anonymously on 0800 555111.
Quote reference number 12180224233 when providing details.