Emergency services were alerted to the incident on Pearl Street at around 2.51pm on Tuesday, 18 July.
Two other people escaped from the building with minor injuries.
It is understood local firm Young Contractors had been working at the site for around three weeks.
Gareth Davies, Area Manager for South Wales Fire and Rescue Service, said: "At 14:51 today (18 July), South Wales Fire and Rescue Service was alerted to a collapsed structure incident, with a person trapped, on Pearl Street in Cardiff. SWFRS crews were in attendance within four minutes of the initial call.
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"Two persons self-rescued at the incident with minor injuries, and SWFRS crews worked strenuously, along with the highly experienced All Wales Urban Search and Rescue (USAR) team to undertake a search. A man was sadly found trapped within the collapsed structure and tragically lost their life.
"In the coming hours, SWFRS and the All Wales USAR specialist rescue teams will be working to extricate the gentleman and supporting South Wales Police and other partner agencies in their investigations.
"As a Service, we wish to extend our sympathies to the individual's family at this very sad time."
(LM)
