Kent Police and paramedics were called to the track near Dartford at 3pm on Saturday after a racing car spun off the track during a British Automobile Racing Club (BARC) Car Championship and hit two people.
One man in his 60s was declared dead at the scene.
The second person and the driver of the car were taken to a local hospital for treatment.
An investigation into the incident has begun. A police spokesperson said no suspicious circumstances were being reported.
Reacting to the accident, Lewis Hamilton said he was “devastated” to hear of the death, writing on Instagram: “Devastated to hear of the passing of a marshal at the Brands Hatch Circuit.
“These volunteer marshals are what makes racing possible, they are heroes. My heart is with his family.”
F1 driver Lando Norris also described the news as “heartbreaking”. “We wouldn’t be able to do what we do without marshals. They’re the heroes of our sport,” he tweeted.
“My thoughts are with the family and friends of those involved.”
In a statement, the British Automobile Racing Club (BARC) said: “On behalf of everyone connected with the BARC, we are devastated by [the] loss of one of the amazing volunteer marshal community who do so much to enable the sport to take place.
“Our thoughts and best wishes are with the family and friends of all those involved.”
Motorsport UK said it was “deeply saddened” by the accident.
A spokesperson said: “The race meeting was immediately suspended and Motorsport UK, together with the event organiser, has begun a full investigation into the circumstances of the incident.
“The thoughts of everyone at Motorsport UK are with the marshal’s family, the organisers of the event, and other members of the motorsport community who were present.”
Last week, British Superbike rider Brad Jones was placed in an induced coma after crashing in the opening lap of a championship race at the Brands Hatch.
The iForce Lloyd & Jones BMW rider was treated at trackside after sustaining serious head, chest and leg injuries, before he was airlifted to hospital. He remains at King’s College Hospital in London.