The Egyptian army said it would respond with the "utmost severity and firmness and force" if protesters tried to approach or break into its bases.
Thousands of Islamist supporters of deposed President Mohammed Mursi were demonstrating to demand his return to power.
At least 92 people were killed in the days after the army toppled Mr Mursi on 3 July, though protests have been peaceful for the past week.
Separately, US Deputy Secretary of State William Burns has said the United States will not try to impose its model on Egypt or support specific parties or personalities.
Mr Burns, making the first high-level visit to Egypt by a US official since the army forced Mr Mursi from office, said he did not think the country was in danger of repeating the tragedy of Syria, where more than 100,000 people have been killed in civil war.
Meanwhile, newly-appointed Egyptian government minister Ashraf al-Arabi has said that aid from Arab states will carry Egypt through its transition period, and it does not need to restart negotiations with the IMF.
Mr al-Arabi, a US-educated economist who served in the same post under deposed President Mohammed Mursi until May, joins a government led by liberal economist Hazem el-Beblawi.
Since Mr Mursi was toppled, Saudi Arabia, the United Arab Emirates and Kuwait have offered Egypt €9.9bn in cash, loans and fuel aid.
Egypt was negotiating with the IMF last year for a €3.6bn loan programme, but did not reach agreement despite months of negotiations.
The Egyptian economy has been hit hard by street violence and political turmoil since a 2011 uprising against former leader Hosni Mubarak.
A general in the police force has been put in charge of Egypt's supply ministry, which manages its system of distributing state subsidised food and fuel.
Egypt is the world's biggest importer of wheat and also buys diesel to distribute to the population at subsidised prices.