The camps had been occupied by supporters of former president Mohamed Morsi, who was deposed in early July.
The health ministry says 149 people have been killed. But the Muslim Brotherhood, which was behind the protests, says more than 2,000 died.
The state of emergency is scheduled to last for a month.
It imposes a curfew in Cairo and several other provinces between 19:00 local time and 06:00.
The measure was taken because the “security and order of the nation face danger due to deliberate sabotage, and attacks on public and private buildings and the loss of life by extremist groups,” the presidency said in a statement.
In the wake of the violence, Vice-President Mohammed El Baradei has announced his resignation from the interim government.
Armored bulldozers moved deep into the main protest camp outside Cairo’s Rabaa al-Adawiya mosque shortly after dawn on Wednesday morning.
Officials say another protest camp, at Nahda Square, has been cleared and a mopping-up operation in the surrounding streets was under way.
Reporters described wounded protesters being treated next to the dead in makeshift field hospitals.
The 17-year-old daughter of leading Muslim Brotherhood figure Mohamed el-Beltagy was among the dead, reports say. Asmaa el-Beltagy was shot in the back and chest, her brother said.
A cameraman working for Sky News, Mick Deane, has also been killed – as has a reporter for Gulf News, Habiba Ahmed Abd Elaziz.
The White House condemned the bloodshed, saying it “runs directly counter to the pledges by the interim government to pursue reconciliation”.
UN Secretary General Ban Ki-moon urged “all Egyptians to concentrate their efforts on promoting genuinely inclusive reconciliation”, his spokesman Martin Nesirky said.
There are also reports of unrest elsewhere in Egypt.
It is still unclear how many casualties were caught up in the two Cairo operations. Figures differ widely and have been impossible to verify independently.
The health ministry has issued an official death toll of 95.
The interior ministry earlier denied any deaths were caused by its forces firing live ammunition.
“Security forces used only tear gas canisters to disperse the protesters though it was heavily fired at by armed elements from inside the two protest camps, causing the death of an officer and a conscript and the injury of four policemen and two conscripts,” the ministry said in a statement.
The government had congratulated the security forces on their operation.
In a televised statement, a government spokesman praised their “self-restraint” and spoke of the “smaller number” of injuries among protesters.
The government would decisively confront attempts to attack state buildings and police stations, he said.
Supporters of Mohamed Morsi have been occupying Nahda Square and the Rabaa al-Adawiya site since he was ousted on July 3. They want him reinstated.
Large plumes of smoke rose over parts of the city as the operation to clear the camps began, with tear gas canisters fired and helicopters hovering above.
Muslim Brotherhood TV called for people to send cars to the sit-ins to take casualties to hospital.
Several Muslim Brotherhood figures have been arrested, security sources said.
There has been strong international reaction to the storming of the camps.
White House spokesman Josh Earnest told a news conference that the administration had repeatedly urged the Egyptian military and security forces to show restraint, and strongly opposed the declaration of a state of emergency.
The European Union called the reports of deaths and injuries “extremely worrying”.
A statement issued on behalf of EU foreign policy chief Catherine Ashton said: “We reiterate that violence won’t lead to any solution and we urge the Egyptian authorities to proceed with utmost restraint.”
Turkish PM Recep Tayyip Erdogan described the result of the camp clearances as a massacre, accused other countries of paving the way for the violence by staying silent, and called for the UN and the Arab League to act immediately.
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