Officers attended a report flammable liquid has been thrown at a barbers in Upper Tooting Road at around 18.45 on Friday 27 August.
They discovered a small fire had started outside the venue but no significant damage was caused and no one was injured.
It is believed that following the incident, a male suspect ran from the scene into Brudenell Road where he got into a car and left.
You can view the CCTV image on our Radio Jackie website, anyone with information is urged to call police on 101.