One lane of the busy Wakefield Road, near the junction with Leeds Road and Dewsbury Ring Road, was closed during rush hour on Monday.
Drivers were left holding their noses as they negotiated the smelly obstruction.
The smell wafted around the town centre, carried by the breeze.
Kirklees Council sent a cleansing team to clean up the mess and now want to send the driver the bill.
In a statement, a council spokesman said: “We had a number of calls due to this incident, but because of the amount of muck that was left in the road, the Highways team had to use a JCB and temporarily close part of the road.
“The cleansing team then used a sweeper to clean the surface before the road was re-opened.
“We have some information and will aim to recover our costs from the driver of the vehicle that dumped the waste.”