The West Midlands Police has launched a murder investigation into the incident. A man has tragically died. Five others were also injured, according to the police.
The first stabbing was in Constitution Hill, police said, and the suspect then moved from north to south, to Livery Street, Irving Street and ending at Hurst Street.
Sky reporter Lape Banjo said those who were injured are being treated at local hospitals. "Detectives are following a number of lines of enquiry and we've increased our uniformed and armed response in the city", the police said.
"We are aware of a number of injured people, but at the moment we are not in a position to say how many or how serious".
The latest incident comes amid concern about levels of knife crime in Britain, particularly in the capital, London.
The final location is an area known as the city's Gay Village, where people had been seated at outdoor tables eating and drinking. Cordons are in place, and there are some road closures.
"The emergency services have well-rehearsed plans for dealing with major incidents". That was soon followed by reports of other stabbings across the city center over a period of about two hours.
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"We immediately attended, along with colleagues from the ambulance service", the force said in a statement.
"My thoughts are with the families of those hurt, particularly of the man who tragically lost his life". More info as we get it.
Police investigations are ongoing.
Chief Superintendent Steve Graham termed the stabbing incidents "tragic, shocking and understandably frightening".
"Please be assured that we are doing absolutely everything we can to find whoever was responsible and try to understand what exactly happened". This has been declared a major incident.
"Your safety is our priority". We are aware of reports on social media.