Firefighters from Hampshire and Isle of Wight Fire and Rescue Service were called to the scene in Horton Heath at 8.15am.
The cause of the fire is believed to be peroxide hair dye product which heated to over 100 degrees under compaction, and then ignited.
It took fire crews 45 minutes to make the load in the lorry safe before the blaze was extinguished.
No one was injured in the incident.
Eastleigh Borough Council is warning residents not to dispose of waste which could be a fire hazard.
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A spokesperson for the council said: “The vehicle was returned to the council’s Hedge End Depot where it was tipped.
“We are now working with Hampshire County Council and Veolia to co-ordinate the disposal of the waste.
“Residents are being advised that peroxide is a fire risk.
“A better option for peroxide disposal is treating it as hazardous waste and taking it to a Hazardous Waste Recycling Centre with a hazardous waste container, which can be found at locations across the county, including Netley, Segensworth, Winchester and Southampton.”
