Five further arrests were made in the city as violence broke out after the match, while three arrests were made at Walsall's home match with Port Vale.
The 30-year-old Smethwick man was arrested a short time after the assault, just before the 3pm kick-off on Saturday, which left a 60-year-old Millwall fan seriously injured.
It is believed that the victim, from London, was with his family and had just arrived at the home of Birmingham City when he was assaulted on Cattell Road.
West Midlands Police that they were working closely with both football clubs and were supporting the man's family.
Three men were also arrested at the Walsall v Port Vale match on Saturday. Two were held for a short period to prevent a breach of the peace while the third was arrested on suspicion of causing fear of violence.
Following the Birmingham v Millwall match police arrested five people as fights broke out across the city. Around 150 seats inside St Andrew’s were vandalised during the game.
A police spokesperson said: "We had a large operation in place for the fixture but incidents broke out across a large area of the city.
"The level of violence - which our officers put themselves in the middle of to protect people - meant some of our officers had to wear public order helmets, use shields and draw their batons, while continually warning people to move away.
"We understand how the scene may have scared people who had nothing to do with the violence.
"Bricks, bottles and objects were used as weapons in the hotspots around Digbeth and other areas between the stadium and New Street railway station.
"Our Football Policing Unit and detectives from Force CID have opened a joint investigation. They are working closely with both football clubs and supporter groups.
"More arrests will come in the following weeks meaning anyone involved should immediately go to their local police station to explain what happened.
"Witnesses have been spoken to and CCTV is being reviewed alongside images posted online.
"Five men have been arrested on suspicion of a variety of offences including non-recent offences at football matches, racism, violent disorder and public order crimes."
Chief Superintendent Ian Parnell said: “It is important to remember that despite how disruptive these incidents were and the fear they caused others, the behaviour of these people represented a minority.
“The violent behaviour was unacceptable and we will do everything we can to find those responsible so that they can be punished appropriately by the courts.
“We always push for the maximum punishment and we are supported by the clubs in this.
“Most fans just want to enjoy the game but a minority have ruined today for the majority.
“In addition to the impact criminal convictions have on jobs, future careers, travel rights and more, people found guilty of football related crimes risk lifetime bans from all games.
“There was a large operation in place for today’s three games. Officers from across the West Midlands were called in to help, supported by dog units, drone teams and others, and cancelled days off. The clubs were each involved in creating and supporting those plans.
“Our preparations meant that we successfully stopped lots of incidents before they started and most people will never know about those.
“The security plans and the bravery of our officers also meant that we were able to quickly get things back under control in the multiple, sporadic locations covering a large area where people were intent on violence.”