Videos shared online over the weekend showed a person jumping from the Iron Bridge in Ironbridge, into the River Severn below.
The person could be seen climbing onto the railings of the historic bridge before turning their back to the river, balancing their toes on the edge and performing a backflip into the water.
A number of people could be see watching the efforts from the individual, who appeared to be wearing a wetsuit for the jump.
English Heritage, which is responsible for looking after the bridge – one of the UK's most important historic monuments – said it was 'alarmed' to see the incident.
The organisation's Free Sites Partnership Manager, Helen Allen, said there were concerns about people injuring themselves doing the activity, and about potential damage to the bridge itself.
She warned people not to try the same thing in future.
She said: "We were alarmed by reports of this incident, which involved individuals putting both their own safety and the historic ironwork of the Iron Bridge at risk.
"By undertaking such reckless activity in pursuit of an adrenaline rush, the perpetrators could easily have badly injured themselves, or caused many thousands of pounds of damage to the bridge’s brittle cast ironwork.
"We discourage anyone considering similar actions in the strongest possible terms.”
The Iron Bridge is a Grade I listed structure, with work on the bridge starting in 1777, before opening in 1781.
It is a major tourist attraction, bringing thousands of people to the county every year and is a major part of the Ironbridge Gorge World Heritage Status.