Superintendent Andy Parsons, of West Midlands Police, said: “Officers spotted the man acting suspiciously and spoke to him. At this point they have arrested him.
“The man was carrying a bag, and as a precaution Victoria Square, where the vigil was being held, was cleared for around 15 minutes.
“A small axe was recovered along with a large stick."
The arrested man was known to officers and thought to have a history of mental health problems, a police spokesman said.
Supt Parsons said: “We will be interviewing the man to understand his intentions after mental health experts have assessed his condition."
He added: “I’d like to thank people for the calm and collected way in which they responded to the incident. The professionalism of our officers who responded to the incident is also commendable and indicative of British policing.”
Thousands gathered at vigils across the country on Tuesday evening in a show of defiance after a suicide bomber targeted crowds at an Ariana Grande concert at Manchester Arena.