Passengers driving to the airport have been warned to allow extra time or find a different route.
An airport statement said: “Delays are expected, please allow extra time for your journeys.
“A signed diversion route will be in place.”
A Jet2 statement said motorists were “advised to avoid this section of the M62” and plan an “alternate route”.
National Highways also advised drivers to “plan ahead and allow more time to complete” their journey.
The 138ft (42m) long Castleton bridge is used by trains travelling from West Yorkshire to Greater Manchester.
