The smaller, two-story edifice was a Salvation Army store. The cause of the collapse not far from city hall was not immediately known, but authorities said it appeared to have been an industrial accident.
"Thirteen people have been recovered and transferred to hospitals. Unfortunately, we have one confirmed fatality," a Philadelphia Police Department spokesman told AFP, adding that the victim was a woman.
No one was trapped under the rubble and fire chief Lloyd Ayers said those taken to hospital suffered only "minor" injuries.
Fire chief Lloyd Ayers said workers would continue clearing the debris in what he predicted would be a "12 to 24-hour operation."
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"It is delicate. This is dangerous work," Mayor Michael Nutter said.
The mayor said officials were unsure how many people were in the Salvation Army store, a charity shop that primarily serves the poor, during the accident.
The other building, which only had its walls still standing, was being demolished.
Marc Newall, 46, ran to help from his nearby workplace after the collapse.
He joined others in clearing the debris covering two women, and said that within 20 minutes after the Fire Department showed up, five people were rescued from under the collapsed building.
"It was a knee-shaking experience," Newall said.