Emergency services were called to the A895 where the bridge was closed around 3pm.
Drivers were being advised to take an alternative route and can expect longer journey times than normal.
Police Scotland tweeted at the time: “Due to an ongoing Police Incident the A985 Kincardine Bridge is currently closed in both directions.
“Diversion via Clacks Bridge.”
Earlier in the day around four miles of the M90 was shut in Fife, between junctions 3 and 4.