The deadly incident occurred as Egyptian security forces tried to disperse the protesters from Liberation Square on Monday, killing three more protesters in the process.
The Monday violence brought the four-day death toll to at least 14. More than 500 others have been injured in clashes over the past days.
The recent clashes first broke out on Friday in and around Liberation Square outside the parliament building and the headquarters of the government between ruling military troops and Egyptian civilians.
The protesters had camped outside the cabinet offices since late November to prevent Ganzouri from entering.
The angry demonstrators demand an end to the ruling military council’s power and want the establishment of a civilian government.
They accuse the military junta of carrying on with practices of the decades-long regime of ousted dictator Hosni Mubarak.