Newport Quay bridge would normally be used by traffic leaving the Seaclose Park festival ground and by coaches bringing visitors to the town's market.
Large traffic and coach operators have been advised of a diversion via Seaclose where there is a 10mph limit.
Isle of Wight Council said the festival site was still being cleared after the four-day event which ended on Sunday.
It is not yet known how long the bridge will remain closed.
Islanders are already facing diversions after continuing problems with the Cowes "floating bridge" chain ferry further downstream.
A bridge near the Isle of Wight Festival site has been closed after it was declared unsafe for large vehicles.