Investigators say the theft happened Sept. 29 at a Shake-A-Paw store at 1 Atlantic Avenue.
The suspect stole an 8-week old white/cream colored Maltese Poodle valued at $995, and exited the store in an unknown direction.
Nassau County Crime Stoppers and the Lynbrook are asking anyone with information about the theft to call their toll-free hotline, 1-800-244-TIPS.
There's a $5,000 reward for information leading to an arrest.