The leaflets said the patient had been referred for an urgent appointment as their symptoms might indicate cancer.
East Sussex NHS Trust has put the mix-up down to an external company that distributes its printed material.
It said the wrong patient information leaflets were added to hospital appointment letters sent out in March.
It has now contacted everyone affected to apologise and explain what went wrong.
Liz Fellows, assistant director of operations at the trust, said: "It was an administrative error and we apologise for any unnecessary anxiety this error may have caused."
East Sussex Healthcare NHS Trust covers Hastings, Eastbourne and Rother, and is responsible for the Conquest Hospital and Eastbourne District Hospital.
The trust said that due to the large number of appointment letters it sends out it uses an external printing company to print and distribute appointment letters.
It said each letter is coded to indicate any supplementary information that needs to accompany it.
Ms Fellows said: "Unfortunately, for a short period in March, the printing company inadvertently miscoded approximately 850 letters resulting in a 'two-week information leaflet' being inserted with an appointment letter.
"As soon as the error became apparent it was stopped immediately, and letters of apology sent out."
Hospital bosses in Sussex have apologised after about 850 patients were sent leaflets in error suggesting they might have cancer.