Manwar Hossain, 22, was ironing clothes in one of the garment factories housed in the nine-storey building outside the Bangladeshi capital when it collapsed on April 24, killing more than 1,100 people.
Hossain was among several thousand people pulled from the rubble at the time of the accident and taken to hospital.
"He was rushed here unconscious and died in a coma (last) Thursday," Zahidur Rahman, a director of the Enam Medical College and Hospital told AFP.
The death toll from the disaster in the suburb of Savar, just outside the capital Dhaka, has risen from 1,129 to 1,134 in recent weeks, as more people died of their injuries, Abdur Rashid, a local government official told AFP.
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More than 3,000 workers were on shift at the Rana Plaza complex, where they made clothing for Western retailers including Britain's Primark and Spain's Mango, when it collapsed.
The tragedy highlighted the appalling safety conditions in the world's second largest garment industry after China and forced Western retailers and the government to promise factory safety inspections.
Scores of distraught relatives are still waiting for news of missing loved ones after the disaster, with 329 people still officially unaccounted for, Rashid said.
Many of them are thought to be among the bodies recovered from the rubble that were too badly damaged or decomposed to identify.
Some of the unidentified bodies were buried at a graveyard in Dhaka after DNA samples were collected. The samples will eventually be matched with those taken from relatives of the missing to confirm their identity and compensate families.