A spokesman for the Palestinians living in the Baladiyyat neighbourhood in the Iraqi capital said the shell exploded in an apartment at 7:30pm (16:30 GMT).
Some 1332 Palestinian families live in the capital's Baladiyyat district, he added.
The US military earlier confirmed that a series of explosions rang out across Baghdad, without providing any further details.
Senior occupation officials in Iraq have warned that the country could face an increase in guerilla violence as millions of Muslims celebrate Eid al-Adha, the feast of sacrifice which begins on Sunday.
The Dutch embassy in Baghdad was engulfed in flames late on Friday after a rocket-propelled grenade struck the unoccupied building in in what the Hague described as a clear target against the Netherlands.
On Wednesday, a bomb hidden in an ambulance blew up outside a hotel housing an interim minister in an upmarket district of al-Karrada.
On January 18, at least 24 people were killed when a truck bomb was detonated outside the entrance to the occupation force headquarters.