A number of witnesses said police closed the road over St George's Bridge in both directions just before 8pm.
There were reports that a man was spotted on top of the bridge amid concerns for his welfare but this has not yet been confirmed by police.
One motorist said she saw a "man on the other side of the barrier."
She added: "People had just got out of their cars heading towards him.
"I pulled over on Marsh Gate near the Three Horse Shoes and called the police. There was another lady there doing the same.
"The police had already had several calls and were en route. By the time I pulled out of the parking area they had cordoned off the bridge heading into town."
We have contacted South Yorkshire Police and are awaiting a reply.
We will bring you updates as and when we get more details.