The George Street incident comes as a separate incident is being dealt with at the Mound, with bomb squad in attendance as a number of streets in the area are sealed off.
Ambulances have been spotted at the corner of George Street near St Andrew Square, while paramedics tend to a casualty near a bus.
A Police Scotland spokesperson said: “Around 3.15pm on Monday, 20 September, we received a report of a crash involving a bus and a pedestrian.
“Emergency services are currently in attendance.”
Updates to follow.