Sisi, promoted from general this week, was empowered by the Supreme Council of the Armed Forces to run for president of Egypt.
Sisi took power in July when the military removed former President Mohamed Morsi, a Muslim Brotherhood member, from office.
"Now the illusion has been pierced [and] all hidden secrets revealed," the Muslim Brotherhood said in a statement posted on its website. "It has become evident that what happened on July 3, 2013, was indeed a full-fledged military coup d'etat."
SCAF took power after longtime President Hosni Mubarak resigned in the wake of Egyptian protests in 2011.
Morsi took office in 2012 after Egypt's first-ever democratic election. He was later criticized for favoring principle embraced by the Muslim Brotherhood.
Sisi was backed this week by former Egyptian Prime Minister Ahmed Shafiq, who lost to Morsi in the 2012 campaign. Amr Moussa, former secretary-general of the Arab League, endorsed the ruling general this month.