Joanna Yeates was filmed on CCTV buying a pizza from Tesco
The discovery was made by a couple walking their dog at Longwood Lane in the Failand area of North Somerset, an Avon and Somerset Police spokesman said.
A police spokesman said: "At 9am this morning a couple walking their dogs found the body of a young woman in a roadside verge in Longwood Lane in the Failand area of North Somerset.
"The area has been cordoned off and Longwood Lane has been closed at both ends by police, pending an examination of the scene by crime scene investigators.
"A pathologist will be attending the scene to examine the body.
"At this moment in time it is far too early to confirm the cause of death or any circumstances."
An operation is now underway to retrieve the body - which has not been identified - without disrupting any evidence at the scene.
Ms Yeates has not been seen since 17 December, when it is believed she returned to the flat she shared with her boyfriend.
Earlier this week Ms Yeates' distressed parents said they believed their daughter had been abducted.