The CentralWorld page said its fire fighters put out the blaze at 6.10pm, about half an hour after it started.
The Central World Complex, which includes a shopping mall and a hotel frequented by tourists, at Bangkok's busy Ratchaprasong intersection was evacuated, said operator Central Pattana.
By 9 pm, the number of people injured had reached 17, said the Erawan Medical Emergency center. He later said that two people were confirmed dead, but did not explain the discrepancy.
The fire broke out on the eighth floor of the hotel, which was used to store documents.
At least one of those who died had fallen from the building, local reports and witnesses say.
Images showed large flames raging out of what appeared to be a rear portion of the complex.
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The blaze started at the Centara Grand hotel and CentralWorld shopping plaza, with people reportedly seen jumping from buildings.
The fire broke out during the congested city's evening rush hour.
Other clips showed emergency services struggling to get through gridlocked rush-hour traffic to get to the scene.
Rescue workers work after the Central World Complex was evacuated due to a fire, in Bangkok April 10, 2019. It's near the main junction for Bangkok's elevated train lines, as well as the Erawan Shrine, which was the site of a deadly bombing in 2015.
The mall is owned by Central Group, which is controlled by one of the wealthiest families in the country.