The incident, apparently due to a gas leak in the building, occurred at 9.30 am, Rosario civil defence director Raul Reinone told reporters.
"So far there are six people dead and at least 58 others with injuries of varying degrees of severity. There are people missing. We are trying to rescue all who may be in the rubble," provincial health minister Miguel Cappiello told television channel Todo Noticias.
Hours after the accident occurred, people were still trapped inside the building, where shouting could be heard from inside the rubble, firefighters reported.
The blast wiped away the front of the edifice, leaving the insides of people's homes and gutted balconies visible from the street below.
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Scenes of panic abounded as sirens wailed and people ran through the streets or gawked at the ruined structure, some of them crying.
Shards of shattered glass littered the streets.
Rosario's health ministry declared an emergency, calling all dispatchers into action.
Mayor Monica Fein said 17 ambulances were on the scene to help people burned in the fire.
People within a two-kilometre radius of the explosion, including 11 schools, were evacuated, as the gas supply to the building could not be cut off.
He said that the magnitude of the event may cause the building to collapse.
"The shock wave was tremendous," the superintendent of a building 200 meters from the site of the explosion told the TV station C5N.
The blast sent flames roaring through the building, as fire truck sirens sounded and traffic clogged Rosario's city centre.
Windows shattered in buildings in a radius of several hundred meters from the blast site. The area includes shops, schools and banks.