Prosecutor General Ruslan Kravchenko, writing on the Telegram messaging app, also said two police officers had been issued "notices of suspicion" after an examination of video from the scene, which showed them running away instead of dealing with the incident's aftermath.
A Russian-born man opened fire on passersby with an automatic rifle on Saturday before barricading himself with hostages in a supermarket, where he was shot dead by police.
"Sadly, a man died in hospital today from injuries he sustained and became the seventh victim of the terrorist act," Kravchenko said on Monday.
He said an armed police patrol team had been called to the scene, but failed to act to stop the shooter or help the wounded.
"Instead, the patrol team, equipped with firearms and all the legal grounds to use them, in fact left the scene," Kravchenko wrote.
"Because of the police officers' failure to take action, the man continued to move unhindered down the street and shoot at defenceless pedestrians."
Earlier, Mayor Vitali Klitschko said seven people, including a child, remained in hospital after being wounded in the shooting in the capital's leafy Holosiivskyi district. Four were in intensive care.
Such shooting incidents are extremely rare in Ukraine, and the country's security service said it was being investigated as a terrorist act. Police have not yet identified a motive for the shooting.
The shooting has raised questions both about the public's right to self-defence and about how the gunman was able to obtain a firearms permit, Interior Minister Ihor Klymenko has said.
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