The male officer’s neck, face and hand were slashed with the knife during the incident at HMV shortly after 9am today.
He has been taken by ambulance to hospital, where he is receiving treatment for his injuries.
A police spokesman said the injuries were not considered to be life-threatening.
He said: “The suspect, a 36-year-old man from Leeds, was detained by store staff and has been arrested in connection with the incident.”
The store was closed while a forensic examination of the scene took place, but it reopened at around 11.10am.
The attack was reported at 9.07am, just a few minutes after the store had opened for the Black Friday sales.
Anyone who witnessed the incident is asked to contact Leeds District CID via 101, quoting log number 344 of November 25.