Many more - who were in the building when it caved in - were feared to be dead, including a group of children.
Their bodies have yet to be pulled out from the mass of broken concrete beams and twisted steel reinforcement rods that remains.
Dozens of rescue workers are continuing to clear the rubble.
The Interior Ministry said that the dead included factory workers and several firefighters, including the city's fire and disaster chief General Mohammed Ragai.
At least 38 factory workers and firefighters were also injured, officials at the city's Muwasa Hospital said.
A mass funeral for 12 of the victims was held at a mosque in Alexandria on Thursday.
Collapse
Firefighters were investigating the cause of the fire when the building collapsed, senior civil defence official Amar al-Denawy said.
Eyewitness Walid al-Beheiry told the AFP news agency that it took firefighters seven hours to put out the fire.
He said the collapse occurred after the fire appeared to be put out.
"You couldn't see any fire at the end but you could still see smoke," Mr Beheiry said.
"A bunch of young children got into the factory so they could take clothes and, in seconds, the whole six storeys collapsed, trapping them."
Police said the fire was believed to be started by an electrical short circuit. Initial estimate put the cost of destruction at $2.5m.
Local reports say the incident caused cracks to appear in a neighbouring factory.