Police believe the male, identified as 17-year-old Francisco Garcia, stole the dog at the facility on North Robert C. Lanier Drive around 12:13 p.m. Tuesday.
The puppy was in the process of being adopted by a family when she was abducted, police said.
Authorities say Garcia was issued a citation for theft, but the location of the puppy remains unknown.
Anyone with information is asked to contact Baytown PD at 281-422-8371.