Police were called to the scene at 5.22pm on Monday after a bicycle and a black Audi TT collided opposite the Esso garage.
The male cyclist, who was found in Old Torrington Road, was taken in a stretcher to North Devon District Hospital with suspected neck injuries.
A passerby said: "I was cycling past the roundabout at the top of Sticklepath Hill when I saw a cyclist lying on their back on the road and the emergency services in action.
"The bike was lying on its side and an ambulance paramedic was giving CPR.
"Another member of the ambulance crew was getting out a spinal board.
"The cyclist, not moving, was partly covered with a blanket so I couldn't tell if it was a man or a woman.
"It didn't look like anyone else was injured and the traffic was still flowing. I assumed he had been knocked off his bike. I hope they're all right, whoever it is."
The road was closed while police dealt with the incident.