Initial reports from Cairo said 33 people were injured on Monday as firemen attempted to contain a blaze which had spread to a restaurant on the ground floor.
Egyptian Health Minister Ismail Sallam said no one had died in the collapse, but witnesses said they saw one body being pulled from the rubble.
Firefighters, policemen and civil defence officers immediately began sifting through the rubble to find possible survivors.
After a visit to the building in the residential suburb of Madinat Nasr, Cairo Governor Abd al-Rahim Shihata said that it was too early to give a final toll.
The building collapsed after the spread of a fire which started in the cellar of the high-rise building.
Gas containers and other flammable materials caused several explosions and might have weakened the structure.
But Housing Minister Ibrahim Sulayman, who visited the site of the tragedy, said seven of the 12 storeys had been constructed illegally after 1981.
Such collapses are a frequent occurrence in Egypt, where many buildings are built without authorisation or normal checks, while many others have simply fallen into neglect.
Seven people died when another suburban building collapsed in May last year.