Officers arrested the 28-year-old at the city centre destination on suspicion of possession of an offensive weapon.
The centre was evacuated for around half an hour when a suspicious bag was found.
However the bag was later found to contain toiletries, West Midlands Police said.
The force took to social media at shortly after 9.30am to confirm the centre had reopened.
#BULLRING | The Bullring was evacuated briefly this morning after a 28-year-old man, armed with a machete, was arrested on suspicion of possession of an offensive weapon. A bag left in the centre was initially thought to be suspicious, but found to contain toiletries. @Bullring pic.twitter.com/369LQamPkP— West Midlands Police (@WMPolice) June 24, 2020