Humberside Police have issued the appeal after the incident happened at 9.40am this morning (Saturday).
The vehicle which the ladders fell from carried on driving.
The statement said: "We’re looking for witnesses to a road traffic collision that happened at 09:40 on Saturday 8th July on the west bound carriage onto the Ouse Bridge.
"The collision happened when some ladders fell from a vehicle into the middle and outside lane, causing damage to several vehicles. The vehicle which shed the ladders did not stop and we would like to trace the driver.
"The road has now been cleared.
"If you saw anything please call 101 quoting log 211 of 08/08/2017"