"He has been described as in his late 30s or early 40s, approximately 167cm tall (5'6") and of a thin build.
"He has no facial hair, and was wearing black gloves at one point during the incident," police said.
It is not known if any unpaid-for food was taken in the incident.
Police have asked anyone who knows who the man is, or who saw a man matching the description, to contact Detective Elliot Western at the Christchurch Central Police Station on 03 363 7400.
Alternatively, information can be provided anonymously via the organisation Crimestoppers on 0800 555 111.