The building's collapse in the Nile Delta city of Damanhour was preceded by a "gas pipe explosion," according to a brief government statement.
Search efforts were underway to find those still missing beneath the rubble while the injured were transported to a nearby hospital, it said.
No further details were immediately provided.
According to reports in local media, the two killed were children.
Building collapses are common in Egypt, where poor construction and shoddy building maintenance are common across the country, especially in shantytowns, low-income neighbourhoods and rural areas.
Last month, six people were killed in an apartment block collapse in the southern city of Asyuit.
The government has tried to crack down on illegal construction in recent years following decades of lax law enforcement.
Also, authorities are building new cities and neighbourhoods to rehouse those living in poorly constructed buildings.
However, many cities across the country still have large swaths of unlicensed apartment blocks and shantytowns in breach of building regulations.
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