Rawcliffe Bridge over the Dutch River should have reopened on November 20, but instead will now reopen on Monday December 18, East Riding Council said.
The road is currently closed for specialist inspection works.
Mike Ball, East Riding Council's principal engineer, said: “We do apologise for the inconvenience that this extended closure will cause, but would like to reassure motorists that the works are essential to help to ensure the long term future of the bridge.”
Parish council chairman Robert Barker said: "You have to go with what the principal engineer says - you don't want an unsafe bridge.
"Obviously they have found more things that need addressing.
"It is not ideal in the run up to Christmas, but unfortunately it has to be done."
A diversion route is in place for cars and other traffic, but pedestrians and cyclists can still cross the bridge.
Local businesses can continue to be accessed via the diversion route.
East Yorkshire Motor Services route number 88 will continue to run, but will follow the diversion route during this period.
A shuttle bus will also continue for the part of the journey between Rawcliffe and Rawcliffe Bridge.