Officers believe there was an altercation between a group of young people outside the store before the stabbing happened.
Det Insp Paul Shortt said: “This was an appalling act of violence carried out in full view of members of the public.
“A team of detectives is now working to understand exactly what happened in the moments before, during and after this incident.”
The force asked anyone with any information to get in touch.
A Primark spokesperson said staff were assisting the police investigation and that the store would be closed until further notice.
They added: “Our thoughts are with the victim and we are focused on supporting our colleagues who were in store at the time.”
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