On Thursday night around 1,000 Egyptians burned Algerian flags in a street near the Algerian embassy.
The protests continued into the morning, with 15 cars reported damaged, along with a number of shops. The ministry said 11 police officers were among the injured.
On Friday afternoon, worshippers leaving a mosque in the neighbouring Mohandisseen district gathered after prayers to again burn Algerian flags and chant anti-Algerian slogans.
Algeria beat Egypt 1-0 in a play-off in Sudan on Wednesday.
1978: Egyptian team recalled part-way through All Africa Games in Algeria after brawl following win over Libya. Algerian spectators joined in on Libyan side
1989: Egypt beat Algeria to reach Italia 90. After the match, midfielder Lakhdar Belloumi blinded the Egyptian team doctor with a bottle
1990: Egypt refused to send its team to African Nations Cup in Algeria
2009: Striker Hossam Hassan and brother Ibrahim Hassan banned indefinitely by Fifa after a brawl following a club game in Algeria
Protesters were incensed by reports that Egyptian fans at the match had been attacked as they left the stadium.
"We should treat Algeria like any country that has declared war on us," university student Amr Higazi told Agence France Presse.
The BBC's Christian Fraser in Cairo says demonstrations like this are normally broken up well before they begin.
Meanwhile, Egypt has threatened to quit international football for two years after complaining to world football governing body Fifa over Algerian fans' behaviour in Khartoum.
The statement by Egypt's Football Federation added: "Egyptian fans, officials and players put their lives at risk before and after the game, under threat from weapons, knives, swords and flares."
If Egypt do not go through with their threat, there is a chance the teams could meet again in less than three months in the Cup of African Nations, hosted by Angola.
The two teams were drawn in different groups at Friday's ceremony but could meet each other in the later stages.
Egypt's foreign ministry had summoned the Algerian ambassador to hear complaints about reports of attacks on Egyptian fans in Khartoum and on Egyptian businesses in Algeria.
The Egyptian ambassador in Algiers was than recalled "for consultations".
Sudan has also summoned the Egyptian envoy in Khartoum, angry at Egyptian media coverage of the game's aftermath.
The Egyptian government alleges 21 of its citizens were attacked after the match, but Sudan says many fewer were injured.
The teams needed the play-off in a neutral country to decide on qualification after the final group match between them on Saturday saw Egypt win 2-0, meaning the two teams finished tied at the top of the group with equal points and identical goal difference.
Fifa has opened disciplinary proceedings against Egypt after the Algerian team bus was pelted with stones in Cairo before the match.
Three Algerian players were injured by rocks thrown as they arrived.
Violence between Egypt and Algeria fans flared up across four countries.
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