The accident happened around 11 a.m. in the 1700 block of W. 10th Street.
Witnesses said the blue SUV was speeding down the street when it hit a parked car, launching both vehicles into the building.
"I called 911 and immediately went over to check on the driver of the car," said neighbor Steve Horton, who witnessed the SUV speed and crash. "He was gone. He was expired."
Dallas Fire Rescue officials said all three people who were in the SUV died in the wreck. They have been identified as Lucinda Rosas De Esparza and Paul and Evelina Maltos.
There was one person inside the apartments when it happened, but he was not hurt.
The building had to be reinforced before the vehicles could be removed because of concerns the structure would collapse. Gasoline from the two vehicles poured into the basement, which also had to be cleaned up.
Renters who lived at the property could be seen going in Wednesday evening and removing items from their apartments and then leaving.
It's unknown how long it will take to make repairs to the building.