A male rider came off his bike in the town’s Albert Road, near to Albert Bridge, and collided with the woman at around 11am.
The injured pedestrian was taken by Helimed to Edinburgh Royal Infirmary, where medical staff have described her condition as stable.
The road was closed for a time and Border Buses terminated all services crossing it immediately after the incident.
A Police Scotland spokesperson said: “The male rider of the bike was taken to the Borders General for treatment to leg injuries, the severity of which are not known to us.
“Inquiries are continuing.”
An eye-witness said: “When we passed the poor lady was on the pavement, obviously unable to move.”