The historic building in the northern city of San Miguel de Tucuman collapsed around 8:00 pm (2300 GMT) on Wednesday with heavy traffic in the street outside.
Police first reported one man had been killed but revised the toll after discovering in the rubble two more bodies, those of another man and a woman.
There were no workers in the building at the time and police believe the victims were all passers-by. Two other women were being treated for multiple injuries but were out of danger.
Investigators believe the collapse of the French-style Parravicini theater was due to a problem in the structure that dates from its construction.
It closed in 1995 but had been under renovation for months to turn it into a commercial building.
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