Nottinghamshire Police said the knifeman is still on the run after a suspect fled in the direction of Market Square.
Detective Inspector Paul Shortt, of Nottinghamshire Police, said: “This was an appalling act of violence carried out in full view of members of the public.
Suspect fled the scene and is still on the run after 17-year-old seriously injured in attack.
Officers believe there was a fight outside the store between a group of young people before the attack happened.
A teenage boy has been stabbed in front of horrified shoppers in a Primark store in Nottingham city centre.