The incident happened at Esso petrol station in Dartford Road at around 10.50am today (March 11).
Officers, South East Coast Ambulance Service and Kent Fire and Rescue were called to the scene.
The person was pronounced dead shortly after.
A spokesperson for South East Coast Ambulance Service said: “We were called at approximately 10.50am today to Tesco Express on Dartford Road, Dartford, to reports a person had collapsed.
“Ambulance crews attended the scene but sadly, despite the efforts of all those involved, the person died at the scene.”
