Security officials say that Mohamed Morsi supporters torched two police checkpoints near the south Cairo district of Helwan on Thursday during a protest to mark the first anniversary of the Islamist president's ouster, Al-Ahram's Arabic news website reported.
No injuries were reported.
Ali El-Demerdash, Cairo security head, has ordered the formation of a committee to find those responsible.
According to the head of Helwan's prosecution, Wael Ghanem, hundreds of Morsi supporters took part in the protest. Molotov cocktails were hurled at the checkpoint and caused the fire.
Over 150 Morsi supporters were arrested in Thursday's protests in nine cities nationwide, including Cairo.
At least one pro-Morsi demonstrator was killed and a number of others were injured in clashes with security forces in Giza's Al-Haram district.
A series of homemade bombs went off throughout the day, with two killed in the village of Keradasa, on the outskirts of Cairo.
The leading Islamic coalition supporting Morsi, the National Alliance to Support Legitimacy (NASL), had called for a "day of rage" to mark Morsi's ouster last July.
The government has cracked down hard on Morsi supporters and Muslim Brotherhood members since his ouster last year, with hundreds killed and thousands detained or facing trials, including the Brotherhood's top leadership.
Last December, the Brotherhood was designated a terrorist organisation.