The incident happened outside Iceland at approximately 2pm on Friday, January 16.
A Wiltshire Police spokesperson said: “We attended an initial report of a disorder outside Iceland in Castle Street, Salisbury at approximately 2pm today.
“The victim, a man in his 30s, attended hospital with an injury to his face.”
Two police cars, a police van, and an ambulance were seen at the scene by an eyewitness.
Wiltshire Police said: “Enquiries are ongoing.”