The accident happened on Wyle Cop in the town centre and left the patients needing treatment at the scene as well as Royal Shrewsbury Hospital.
Police say the accident, which happened shortly after 2pm on Saturday, caused the road to be closed for a short time.
A spokesman for West Mercia Police said: "It was a collision between a female pedestrian and a male cyclist, both of who were in their 50s.
"They were both treated but their injuries were not life-threatening.
"The road was closed while we assisted them but it was reopened a short time later."
John Hawker, a spokesman for West Midlands Ambulance Service, said: "We were called at 2.07pm near The Nags Head following reports that a pedestrian and a cyclist had been involved in a collision.
"We sent two ambulances and a rapid response vehicle to the scene.
"Both patients were treated at the scene and transferred to the Royal Shrewsbury Hospital."