Upper Thames Street was closed on the corner of Fish Street Hill around 6am while the situation was dealt with, City of London Police said.
The force told The Daily Star Online the area was reopening around 9am, with one person taken to the Royal London hospital.
CCTV showed just a single person was involved, cops said, and the event was being treated as “non-suspicious”.
The condition of the person involved was unknown.
The incident was “due to an ongoing incident involving a person who has fallen from London Bridge,” cops said in a statement earlier.
They had urged drivers and pedestrians to find alternative routes where possible, with Transport for London announcing some busses had been diverted.
Around 8:45am, TFL added: “Lower Thames Street has reopened westbound near London Bridge after a police investigation.”
They said in a statement earlier: “Route 344 is diverted due to a police incident which has caused Lower Thames Street to be closed westbound near London Bridge.
“Services are diverted via London Bridge, Southwark Street and Southwark Bridge Road.”
TfL Traffic News had added on Twitter: “The A3211 Lower Thames Street is closed westbound near London Bridge due to a police investigation.
“There are short delays on the approach.”
A London Ambulance Service spokesperson said: “We were called at 5:53am today (05 May) to Upper Thames Street, City of London to reports of an incident.
“We sent a medic in a car, an incident response officer and an ambulance crew to the scene.
“We also dispatched London’s Air Ambulance by road.
“We treated a person at the scene and took them to a Major Trauma Centre as a priority.”