London Ambulance Service said one person was taken to hospital after paramedics treated two people at the scene.
A spokesman said: “We were called at 10.10am today [March 5] to reports of a road traffic collision on New Oxford Street, WC1A.
“We sent resources to the scene, including an ambulance crew, a cycle paramedic, an incident response officer and members of our hazardous area response team.
“Our first paramedic arrived on scene in approximately five minutes.
“We treated two people. We took one patient to hospital and discharged the other at the scene.”
A London Fire Brigade spokesman said: “Firefighters are at the scene of a road traffic collision on New Oxford Street in Soho.
“One double-decker bus collided into the front of a building. One man left the bus before the brigade’s arrival and is being assessed on scene by London Ambulance Service crews.
“Road closures are in place and people are advised to avoid the area at this time.
“The Brigade was called at 10.11am. Two fire engines and two fire and rescue units from Soho, Euston and Battersea fire stations are at the scene.”
Transport for London said it was working to remove the bus, with damage understood to be superficial.
A spokesman said: “A route 8 bus has collided with a building on New Oxford Street.
“There were no passengers onboard the bus and we have support available for anyone affected by this incident. We are working with Stagecoach London, the operator, to establish what happened.”
