The four-week-old mongrel pups were stolen from the Smelter Wood Road area of Sheffield.
Two people wearing masks entered the flat, where the owner of the puppies was asleep.
When he was woken, he challenged the pair and they threatened him with a knife, before leaving the flat with the dogs.
No one was injured during the burglary, which happened at around 6.30pm on Monday, February 22.
South Yorkshire Police are investigating the robbery and are appealing for anyone who may have seen the dogs to get in touch.
Officers say they may have already been offered for sale or posted on social media.
Anyone with information is urged to call police on 101, quoting crime reference number 14/33654/21, or alternatively call Crimestoppers, anonymously on 0800 555 111.