On Saturday afternoon during a race meeting at Brands Hatch, an unauthorised private car gained access to the live circuit while the Fun Cup race was in progress.
The race was immediately red flagged and all cars left the circuit.
The arrest comes after a video was posted online of a white VW Polo entering the former F1 circuit during the race.
A police spokesman said: "On Sunday, June 15, Kent Police was made aware of a report of possible offences committed at Brands Hatch race track in West Kingsdown. Officers have today (Monday, June 16) arrested a 21-year-old man from Tonbridge on suspicion of false imprisonment. He remains in police custody."
An investigation into the incident by Kent Police, the Motor Sports Association (MSA) and circuit operators MotorSport Vision (MSV) has been launched.