The video has received almost 40,000 views on Facebook.
Officials say they know the identity of the woman and believe she has abused the pug before.
"She was recently seen walking down the business district in Fairfield and she apparently had the dog by the tail and she was swinging it around," Michael Ramirez of the Solano County Humane Animal Services said.
Officers believe the woman is currently hiding in the Vallejo area.
They hope people who know where she and the dog are will turn her in.