The firefighter who died was last in contact with his colleagues just before 5:30 a.m., The Dallas Morning News reported.
He radioed that he was trapped and lost and then his radio went dead, Dallas Fire-Rescue spokesman Jason Evans said.
Evans said firefighters believe the man became trapped when one of the floors in the apartment complex collapsed.
About 3 hours later, the firefighter's body was discovered in the wreckage, Evans said.
The body was covered in an American flag and removed from the scene.
Two other firefighters were hospitalized with minor injuries, officials said.
At least five residents of the complex were rescued and authorities were trying to determine if all the others had been accounted for.
The fire department received a report about the fire at the Hearthwood North Condominiums at 2:52 a.m.
Strong winds spread the fire.
"It went to six [alarms] at 5:22," Evans said.
"It got defensive pretty fast. At least 24 units in the complex are completely destroyed."