Investigators have been told the man entered the store on Frankston-Dandenong Road around 4.30pm on Tuesday 14 April.
The man waited for employees to be distracted and it is alleged he then used a screwdriver to damage the lock in order to gain access to the puppy pen.
The man took the puppy placing it under his jacket and left the store.
The puppy is described as being 11 weeks old at the time it was stolen, tan and white in colour and is a Cavoodle breed. The puppy is valued at $2000.
Police are investigating the incident and have released a CCTV image of a man they believe may be able to assist with their enquiries.
He is described as being of Caucasian appearance, aged in his late 20s-early 30s, with a thin build, pale skin and brown hair tied up in a ponytail.
He was wearing a black-coloured hooded jacket with black and red-coloured board shorts.
Anyone with any information is urged to contact Crime Stoppers on 1800 333 000 or submit a confidential crime report at www.crimestoppersvic.com.au