The incident ocurred around 9.25pm last night, with access to the bridge closed off to the public.
Police Scotland officers remain at the scene today.
A Police Scotland spokesperson said told newspaper The Scottish Sun: "Officers were made aware of concern for a person near the Clackmannanshire Bridge in Kincardine around 9.25pm on Sunday, 19 January.
"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."
Last night, Fife Police tweeted last night: "Please be aware that the Clackmannanshire Bridge is currently closed due to an ongoing incident.
"Please use an alternative route and we thank you in advance for your patience."