An 18-year-old woman was sent to hospital after an attack in the car park of Tesco in Durrington last night.
According to Sussex Police, officers were alerted by ambulance colleagues at 10.05pm yesterday evening following the attack.
Two people were treated by paramedics, police said.
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An 18-year-old man was treated at the scene for facial injuries and an 18-year-old woman required hospital treatment after being punched and falling to the ground, police said.
A police spokesman said: "Anyone who witnessed the incident who has not yet spoken to police is asked to email firstname.lastname@example.org or call 101 quoting serial 1249 of 02/12."