In a small area surrounding the bridge, there are approximately nine dead geese, which have been there for at least seven days.
It comes amid a devastating wave of avian flu hitting the nation which has led to birds dying all over the country. Last month a bird flu prevention zone was declared across Great Britain.
Bird keepers must now follow strict legal measures to protect their flocks from bird flu, including keeping free range birds in fenced areas and stringent biosecurity for staff on farms.
A spokesperson for Bridgnorth Town Council said: "We have received notification about the geese and the relevant bodies have been notified.
"It is currently with APHA (Animal and Plant Health Agency) who are dealing with the situation as the executive agency of the Department for Environment, Food and Rural Affairs."
APHA will attend the scene in Bridgnorth to take the birds away to be tested. The council said this would happen within the next 42 hours.
Dr James Chipwete, consultant in health protection with the UKHSA (UK Health Security Agency) West Midlands, said: "The A(H5N1) strain is currently the most common strain of bird flu in this country and is highly pathogenic to other birds.
"As a precaution, anyone who has been in direct contact with a sick or dying bird in an area where the infection has been confirmed, will require close monitoring and follow up with UKHSA."