Police cut off side streets, bursts of gunfire were heard and bulldozers and armoured cars were seen moving in.
Security forces fired tear gas and helicopters flew overhead.
The protesters want 62-year-old Morsi, ousted by the military on July 3, reinstated.
The interior ministry issued a statement saying security forces were taking "necessary measures" against the protest at the Rabaa al-Adawiya mosque in the east of Cairo and the protest in Nahda Square in the east.
The interior ministry is keen "not to shed any Egyptian blood", the statement went on.
Large plumes of smoke rose over parts of the city as the operation to clear the camps continued.
The Muslim Brotherhood, which supports the ousted president, put the number of those killed at between 25 and 30.
At least one member of the security forces is among the dead, reports say.
Muslim Brotherhood TV called for people to send cars to the sit-ins to take casualties to hospital.
More than 250 people have been killed in clashes since then.
Yesterday, one person was killed in a confrontation between supporters and opponents of Morsi in Giza after people marched from Nahda Square to a nearby complex of government buildings to protest against the appointment of several military officers as provincial governors.
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