West Midlands Police declared a major incident after officers were called to reports of a knife attack in the early hours of Sunday, with further stabbings then being reported.
One man died, a man and a woman were critically injured injuries and five others were injured.
Detectives believe the stabbings, which took place between 12:30am and 2:20am, are linked and that one suspect was responsible. He remains at large and so far no arrests have been made.
Chief Superintendent Steve Graham said there is “absolutely no suggestion” that the stabbings were “terror-related”, with the attacks on victims appearing to be “random”.
He told a press conference that officers were called to reports of a stabbing in Constitution Hill, north of the city centre, and the suspect worked north-to-south.
He said: "We are still in the early stages of that inquiry but I can say that we are treating all four of those incidents as a linked series.
"We are searching for one suspect and inquiries to identify and then trace that suspect are ongoing."
The two people who were critically injured are still being treated in hospital, Ch Spt Graham said.
He added there was "absolutely no suggestion" that guns were involved and that there was no evidence the incident was motivated by hate towards any particular group nor gang-related.
Mr Graham said no arrests have been made and "significant resources" were being used to track the suspect.
"There was no suggestion that people have seen him running out of the area, searches were being made at the time, and so inquiries and searches were made but unfortunately the suspect wasn't caught and still hasn't been."
All my thoughts are with those affected by the terrible incident in Birmingham last night.— Boris Johnson (@BorisJohnson) September 6, 2020
My thanks to the emergency services who are working hard at the scene. Anyone with information should contact @WMPolice
He added: "Already we've got people going down drains, we've got that level of detailed searches taking place which will hopefully reassure the people that we are doing everything we can do to trace the offender."
Mr Graham added a number of descriptions had come in of the suspect but police were not releasing anything at this time, asking the public to come forward with any information or footage they may have.
Roads closed as police scour streets
He later said there was no known connection between the victims in the four linked incidents and that extra officers have been deployed in Birmingham.
Large parts of the city centre remained cordoned off this morning as a result, including much of the Arcadian Centre, Snow Hill, Hurst Street, Colmore Row and Irving Street.
A small blue police tent could be seen covering a small area of pavement in Livery Street, behind a wide police cordon, right next to Snow Hill station, about half a mile from the Irving Street scene.
About 100 yards away, a second small blue tent was visible in Barwick Street, near the junction of Church Street.
Around the corner in Edmund Street, officers had extended a cordon after removing a drain cover and sifting material.
Among the muck and debris could be seen a black-handled kitchen knife with a serrated blade, which was separated and quickly removed by officers.
A short distance away was what appeared to be a trail of blood spots at the pavement in Newhall Street, leading down to Edmund Street.
In Barwick Street, near Snow Hill train station, two white-overalled forensics officers were placing numbered yellow markers at points on the ground.
They lifted a blue forensics tent near the Utopia Bar and underneath could be seen what appeared to be napkins.
West Midlands Ambulance Service (WMAS) said a large number of resources were sent to Birmingham city centre overnight after the stabbing incidents.
WMAS said 14 ambulances were dispatched, along with 11 paramedic officers, a hazardous area response team, four critical care teams with doctors and critical care paramedics.
A team of St John Ambulance volunteers at the SafeSpace project at the Arcadian were also involved in treating casualties and conveyed one of the patients, WMAS added.
A total of seven patients were treated by ambulance staff - five of which were taken to the major trauma centre at Queen Elizabeth Hospital Birmingham.
Three of the five taken to the major trauma centre had critical injuries and one man was pronounced dead shortly after arrival, WMAS said.
The ambulance service said an eighth patient with minor injuries did not receive ambulance treatment.
Anyone with information is asked to contact WMP via Live Chat or call 101. If you are in danger call 999.