Highways England said they had first been made aware of the fault on the eastbound carriageway at 11am today (Wednesday, June 30).
Problems have been identified with two expansion joints, which are designed to help bridges move slightly when under strain from traffic or changes in air temperature.
Two of three lanes have been closed junction 30 (Rothwell) and junction 31 (Normanton) while engineers inspect the affected joints.
One lane has also been closed at Ouse Bridge eastbound, where the M62 crosses the River Ouse between Goole and Howden, to allow for further inspections.
These closures are expected to remain in place for an "extended period", Highways England said.
More than nine miles of traffic has built up between Wakefield and Leeds while the closures are in place, with traffic now back to junction 27 (Gildersome Interchange).
Drivers are allow for additional travel time if passing through the area.
Highways England Network Operations Manager, Christopher Addy said: “Engineers are on site assessing two bridge joints on the M62. Expansion joints help bridges move under the stresses and strains of heavy traffic and during changes in air temperature.
“The fault occurred at 11am. To safely carry out inspections we have closed two of the three lanes at junctions 30 – 31, and lane one at Ouse Bridge eastbound, which will be in place for an extended period of time.
"The ongoing assessments will help determine when repairs can begin.
“Road signs advising of the delays are in place across the network and drivers are advised to leave extra time for their journeys.”