Emergency teams are still trying to rescue people who remain trapped in the upper floors.
Rescue teams say there is a risk of the apartment block collapsing. Nearby buildings have also been affected.
The explosion was caused by a gas leak in the heating system, Rosario city mayor Monica Fein said.
“The whole front wing of the [10-storey] building collapsed with the impact,” Rosario Civil Defence Director Raul Rainone told the Clarin newspaper.
More than 50 apartments have been totally destroyed in two adjacent blocks.
Rescue personnel are digging through the rubble to try to find survivors.
“I was in the bath when the explosion took place and the ceiling fell over my head. I have lost everything,” a fifth floor resident identified only as Evangelina told La Nacion newspaper.
She said the accident in the Salta street apartment block may well be linked to problems with the gas system.