CCTV footage allegedly shows the man outside the Little Collins Street store just after 2am on Monday, February 24.
Speaking the day after the incident, Senior Constable Bede Whitty said police believed the man broke a hole in the glass without being seen by anyone.
Senior Constable Whitty, who called the alleged act “blatant” and “bold”, said police were unsure how the small hole was created.
It’s alleged the man first used a shorter rod but was unsuccessful, before he left and came back with a longer rod.
The man allegedly took several minutes to create the hole and push the fishing rod through it. When he was disturbed by traffic, police say he walked away from the shopfront, before walking back when it became less busy.