Crowds raced on to the field in the final minutes after a Zamelek goal was disallowed. Nine people were injured during the ugly scenes while television pictures showed the Zamalek players protecting the Tunisian team.
The country's Supreme Council of Armed Forces, handed power after mass demonstrations ousted President Hosni Mubarak in February, ordered an immediate investigation and set up a committee to be headed by the Justice Minister.
The council said it would not accept events that "tarnished Egypt's reputation and its great people" while Egypt's Prime Minister Essam Sharaf and the head of the country's football federation apologised to the Tunisian team.
"The values of the Egyptian and Tunisian people were the primary reason for the success of their revolutions," Sharaf said on the cabinet's Facebook page, referring to the popular protests that also toppled Tunisia's president in January.
"Last night's events do not in any way reflect the position of the Egyptian people towards their Tunisian brothers."
Dozens of Egyptians also gathered in front of the Tunisian embassy in Cairo to apologise for the violence.
Zamalek were winning 2-1 when the Egyptian side's third goal, which would have put them ahead on away goals, was ruled out, angering the home fans who took over the pitch and forced the Algerian referee to leave.
It was the second leg of the round of 32 tie after Club Africain beat Zamalek 4-2 in the first leg.
The incident revived the football tension between Egypt and Algeria after a diplomatic row broke out late in 2009 after an ill-tempered World Cup qualifier between the country's.
The Cairo Stadium had an unusually light police presence for Saturday's match, a contrast to the heavy security presence in football games in the Arab world's most populous nation.
Saturday's events have prompted questions over how Egypt's league can resume without proper security.
Samir Zaher, head of Egypt's Football Federation, said on Sunday that the Premier League season, which was scheduled to resume on 15 April, may be postponed or matches played behind closed doors.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1