Joy City, a 13-storey complex, is the biggest mall in the Xidan area, with global brand names and a large digital cinema. Zhu has been detained and told police that he carried out the attack to "vent personal grievances", according to a statement.
Three men and 10 women were sent to hospital after the attack and one woman died of her injuries, police said.
A man, allegedly motivated by personal problems, has perpetrated a massacre in the center of the Chinese capital, in a crowded place not far from a government building, the state Xinhua news agency reported.
Police detained the man at the scene.
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A video posted online shows a man wielding what looks like a knife and people fleeing in panic.
Perpetrators of similar attacks in the past have been described as mentally ill or bearing grudges against society.
Knives are commonly used because gun controls in China are extremely strict.
The number of injured persons and their conditions remain unknown, the police said.