Katie Fox, 34, was targeted in Smallbrook Queensway, just outside the Bullring shopping centre, shortly before 9:00 pm GMT on Friday.
Djason Raphael, 21, appeared at Birmingham Magistrates' Court on Monday charged with the attack.
He was initially charged with attempted murder, but the charge was upgraded to murder following Ms Fox's death.
The 21-year-old, of Rosedale Avenue, Smethwick, is also charged with two counts of intentionally inflicting grievous bodily harm on October 27 and November 7, possessing a Stanley blade and assaulting a detention escort officer.
Mr Raphael, who appeared before District Judge John Bristow, was told to remain silent after interrupting several times during the six-minute hearing.
He was told he would not be asked to enter any pleas as the offences were too serious to be dealt with at the magistrates' court.
The case was sent to Birmingham Crown Court for a hearing on November 12.
Police said officers would be in the city centre on Monday to reassure the public and investigators are supporting the victim's family.
Detectives are appealing for witnesses who may have seen Mr Raphael, whom they described as a black British man, and who is believed to have been wearing a full grey tracksuit, black cap, trainers and a rucksack.
The stabbing took place outside the Bullring shopping centre, opposite the main entrance to Birmingham New Street station.
Police said they are treating it as an "unprovoked attack" and Detective Inspector James Nix said they are trying to understand why it happened. He described the area as "quite chaotic" and said he and his friends were concerned for their safety.
Ashley Burkes, 25, from Stoke-on-Trent, said he regularly visits Birmingham to see his girlfriend, who lives in the city, and was worried about what had happened.
He said: "It makes me worry about my girlfriend.
"She doesn't drive and works at all the big music venues in the city... and just thinking that something like that happened for no reason, you know, it's terrifying."