Officers were standing guard at the scene - Peacock's Passage, off High Street in Shrewsbury - on Tuesday afternoon.
Police said that a man in his 30s had been treated for a small injury as a result of the incident, which took place at around 12.30pm.
Officers are appealing for witnesses or anyone with information about the incident to come forward.
A spokesman for the police said: "We’re investigating a report of a robbery at around 12.30pm today in High Street, Shrewsbury, when we believe a man in his 30s was approached by an offender.
"Paramedics treated the victim for a small injury. Our enquiries are ongoing at this time but if anyone has any information relating to this incident we would ask them to contact us via our website quoting incident 260i of September 14."
The alley was sealed off by police tape which also surrounds a stretch of the High Street pavement in front of the vegan street food cafe Okra.
A Crime Scene Investigation team has also been at the scene.
Okra had to shut early as a result of the investigation and the cafe told customers on Facebook it would not be back open until Wednesday "due to unforeseen circumstances".
Peacock's Passage connects High Street to Princess Street and is in between Okra and Neal's Yard Remedies.