The lane closures were put in place at about 1.50pm on the M62 Eastbound at Junction 30 Rothwell to J31 Normanton.
This is due to a defect in the bridge joint.
Emergency repairs are ongoing, the AA reports.
The incident has caused huge delays for travellers in West Yorkshire, with long delays reported around Castleford, Lofthouse and Tingley.
There is currently 6.5 miles of congestion, adding an estimated 45 minutes to journey times.
Highways England said: "The M62 eastbound J30 (Rothwell) to J31 (Normanton).
"Two lanes have been closed due to a defect in the bridge joint.
"Traffic Officers are currently at the scene."
It added: "If travelling in West Yorkshire this afternoon please be aware the are LONG DELAYS on the M62 eastbound at Castleford, Lofthouse, Tingley due to this incident.
"There are 6.5 miles of congestion which is likely to add at least 45mins to usual journey times.
"M1 Leeds and Wakefield plan ahead."
The AA has also reported long delays along Barnsdale Road from Methley to Castleford.