The man had demanded a ransom of 200 million euros (more than $A312 million) in cryptocurrencies during the tense, five-hour standoff on Tuesday.
The incident paralysed one of Amsterdam's most popular nightlife neighbourhoods as dozens of heavily armed police surrounded the store, managing to free about 70 people before the suspect was detained.
Police Chief Frank Paauw said the suspect, a 27-year-old man from Amsterdam armed with a handgun and an automatic weapon and wearing camouflage clothing, was run over by police as he chased his fleeing hostage.
Prosecution office spokesman Franklin Wattimena said the suspect died on Wednesday evening. He gave no further details.
The hostage was a Bulgarian man, police said. They didn't release his identity.
"The hostage played a sort of hero's role by, in that split second that he had, forcing a breakthrough in this situation," Paauw said at a news conference.
"Otherwise it could have been a very long and unpleasant night and maybe longer."
After the suspect was run over, a robot checked him for explosives as snipers in nearby buildings took aim, green laser beams from their weapons clearly visible in the night sky.
In contacts with police, the suspect had threatened to blow himself up.
Police on Wednesday said that he had "explosive components," but that they weren't armed.
Paauw said the man had been taken to a hospital with serious injuries, under police guard as detectives investigated his exact motive.
Investigations were continuing, including searching two homes in Amsterdam.
The Apple Store was listed on the company's website as being closed on Wednesday and Thursday. Bullet holes could be seen in the store's windows.
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