Seven fire crews were called when the blaze happened at CJ Wildlife, Upton Magna, shortly before 8am on Tuesday.
Dramatic pictures showed smoke billowing out of the roof of a building at the site as firefighters tackle the flames.
Nobody is thought to have been injured and the cause of the blaze is being investigated.
Shropshire Fire and Rescue Service said that an area of 20m by 50m was "fully involved" in the fire, but station manager Craig Jackson said the early report and "assertive" work from fire crews meant the blaze was contained to a small part of the building.
INCIDENT: Crews have dealt with a large fire nr Uton Magna. Thanks to an early report from staff and the assertive firefighting from crews the fire was contained to a small area of the large building. Fire investigation currently on scene @ShropshireStar @BBCShropshire @bbcmtd pic.twitter.com/k6PYVDsxxg— Craig Jackson (@SFRS_cjackson) January 18, 2022
He said: "Crews have dealt with a large fire near Upton Magna. Thanks to an early report from staff and the assertive firefighting from crews the fire was contained to a small area of the large building. Fire investigation currently on scene."
The fire service's log said: "At 7.48 on Tuesday, January 18, SFRS Fire Control received a call reporting a commercial fire in Shrewsbury.
"Fire involving two-storey brick building. Building approximately 20m by 50m fully involved in fire. Two main jets in use to extinguish fire. Aerial ladder platform and water bowsers in attendance to assist with firefighting operations.
"Seven fire appliances including the aerial ladder platform, the light pumping unit and the water carrier were mobilised from Baschurch, Bridgnorth, Hodnet, Shrewsbury and Telford Central. An operations officer was in attendance."