A Giza prosecution ordered the detention of four members from the political office of April 6 Youth Movement on Monday for illegal protest and firing fireworks, Ahram Arabic website reported.
Earlier in the day, the political movement issued a statement saying that two members from its political offices had been arrested in the early hours of the morning.
Many of the group's members, including founders Ahmed Maher and Mohamed Adel, are currently serving various prison sentences for violating the protest law, pursuant to which protests must be approved by the police in advance.
The move, which was founded in 2008, played an important role in fomenting the 2011 uprising against former autocrat Hosni Mubarak.
The April 6 Youth Movement was named right after the day a mini-uprising took place in the industrial city of Mahalah against Mubarak.
The group was persecuted before the January 2011 uprising but was given a respite after the toppling of Mubarak.
But since the 2013 ouster of Mohamed Morsi, many Egyptian media outlets have denounced the movement, which opposes both the Muslim Brotherhood and the post-Morsi authorities.
A Cairo court banned the group in April 2014.