Security forces were deployed on streets of Cairo including the iconic Tahrir Square - the focal point of the 18-day popular revolt -- to thwart potential protests against President Abdel Fattah al-Sisi's government.
At least 30 Muslim Brotherhood supporters were arrested in Matareya district when they started a march near one of the mosques in the area, officials said.
The supporters were chanting slogans against police and army.
In Alexandria, police dispersed Brotherhood supporters, who marched and chanted against the police and army, demanding the release of ousted Islamist president Mohamed Morsi and other members of the banned group.
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Morsi's Muslim Brotherhood, outlawed and branded a terrorist organisation, yesterday said that it would stage an "unprecedented and unexpected" wave of protests to mark the anniversary.
The situation remained calm in the rest of country as many people stayed home after authorities warned that the January 25 anniversary may witness violent acts.
The uprising that overthrew Mubarak's 30-year-old regime is no longer celebrated after Sisi, then the army chief, overthrew Mubarak's successor Mohamed Morsi in July 2013 and launched a deadly crackdown on his supporters.
Since Sisi installed the new regime, authorities have banned all but police-approved rallies and overseen a crackdown that has left hundreds of Morsi supporters dead and imprisoned thousands.
Hundreds of police and soldiers have been killed in militant attacks since Morsi's ouster and security forces have so far been unable to suppress the insurgency.
The Government supporters handed flowers to police personnel stationed in the Tahrir Square for security.