The 27-year-old suspect was arrested at an address in the Selly Oak area of the city at about 4 a.m., the BBC quoted the West Midlands Police as saying in a statement.
The suspect was also being held over seven counts of attempted murder, the force added.
The attacks happened at four different locations in central Birmingham over 90 minutes in the early hours of Sunday.
Officers were first called just after 12.30 a.m. on Sunday at Constitution Hill, where a man sustained a superficial injury.
About 20 minutes later, they were called to Livery Street, near Snow Hill railway station, where a 19-year-old man was critically injured and a woman was also hurt.
At 1.40 a.m., the police were sent to Irving Street, where a 23-year-old man suffered fatal injuries and another was seriously injured.
Ten minutes later, they were called to Hurst Street, in the city’s Gay Village, where a 32-year-old woman was critically injured and two men were less badly hurt.
The police said they are treating the attacks as “random” at this stage, the BBC reported.
A hotline number and website have been set up for members of the public to provide more information on the attacks, while the sites where the incidents took place remained closed on Monday morning as investigations continued.
Questions have been raised about how the suspect was able to move around the city for 90 minutes.
While Birmingham MP Shabana Mahmood said she “shares the same concerns as everybody else”, West Midlands Mayor Andy Street told the BBC that it was not right to say the police response was too slow.