The incident occurred around 9.25pm last night, with access to the bridge closed off to the public.
Police Scotland officers remain at the scene today.
The bridge was closed as police, coastguard and fire crews dealt with the incident.
A search involving lifeboats and a rescue helicopter was launched.
A Police Scotland spokesperson said: “Officers were made aware of concern for a person near the Clackmannanshire Bridge in Kincardine around 9.25pm on Sunday, January 19.
“The body of a 28-year-old man was recovered from the River Forth a short time later following a search.
“The death is currently being treated as unexplained, although there are no apparent suspicious circumstances. A report will be submitted to the Procurator Fiscal.”