The woman, Zienab Mahmoud, was killed during the clashes in Ain Shams district, a known stronghold for supporters of the ousted president.
Pro-Morsi supporters organised several protests across Egypt as they held their weekly marches after the Friday prayers.
Security forces arrested 35 members of the Morsi-led Muslim Brotherhood in connection with the protests.
The arrested persons possessed Molotov cocktails and cartridge bullets, and were arrested in the governorates of Qalyuiba, Asyut, Minya, Giza and Beheira, a statement issued by the Interior Ministry said.
Egypt has witnessed many bloody clashes between Morsi supporters and security forces since the ouster of Morsi in July 2013, demanding the reinstatement of the Muslim Brotherhood leader.