A Twitter account operated by the Brotherhood, which has largely been driven underground by a massive crackdown, said prisoners have been "banned from family visits, legal counselling, medical care and (live in) overcrowded and unhygienic cells."
Egyptian security forces have arrested thousands of Islamists, including virtually the entire top leadership of Morsi's Muslim Brotherhood, since he was deposed on July 3.
The 85-year-old political and social movement prevailed in a series of polls following the overthrow of Hosni Mubarak in 2011, and Morsi became the country's first freely elected leader after winning elections last year.
The Brotherhood said several senior figures were taking part in the strike, including the wealthy financier and onetime presidential hopeful Khairat al-Shater, senior official Essam al-Erian, former legislator Mohamed Beltagi and Essam al-Haddad, an advisor to Morsi during his presidency.
It did not say whether Morsi himself or the Brotherhood's Supreme Guide Mohammed Badie were also taking part in the hunger strike.
Earlier this month Human Rights Watch said Egypt's military-installed authorities had detained five Morsi aides for nearly five months without disclosing their whereabouts, saying it amounted to an "enforced disappearance.