Kent Fire and Rescue Service was alerted to the blaze in Suffolk Road at 8.14pm on January 18.
The lorry is believed to have been parked in the loading bay of an Aldi supermarket at the time of the incident.
Three fire engines were dispatched to the scene, where crews wearing breathing apparatus used hose reel jets to tackle the fire.
Footage from the scene appears to show the source of the fire located in the cargo holder of the HGV, with flames spreading up the side of the cargo hold’s canvas.
The cause is being treated as suspicious.
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A spokesperson for the rescue service said: “Kent Fire and Rescue Service was called to reports of a lorry on fire at a loading bay in Suffolk Road, Dartford.
“Three fire engines attended and crews, wearing breathing apparatus, used hose reel jets to extinguish the flames.
“There were no reported injuries, and the cause is being treated as suspicious.”
