According to the Centers for Disease Control and Prevention (CDC), it is extremely rare for the Coronavirus to spread from animal to human. They currently believe COVID-19 originated in a live animal market then jumped to humans, but this has not currently been confirmed. The first and only case, that is known, of an animal testing positive for COVID-19 was a tiger at a New York Zoo.
Many common questions for the CDC is "Can my dog or cat give me the Coronavirus?" As of right now, the CDC states there is no evidence that companion animals have the ability to infect humans with COVID-19. They also state they are aware there have been cases outside of the United States of pet reported and thought to be infected with COVID-19 after they were in contact with humans who tested positive for the virus.
The CDC recommends that people who own pets, treat them with the same precautionary measures as humans: no interactions with other people or pets outside of the home, isolate any sick persons from the animal, and practice good hygiene with your pets.
There are more studies being conducted on whether or not animals can transmit the disease to humans.
Information gathered from: https://www.cdc.gov/coronavirus/2019-ncov/daily-life-coping/animals.html