The group, organized by the "No to Women's Oppression Coalition," said it had permission from authorities to deliver a protest letter to the minister of justice, the Sudan Tribune reported Wednesday.
Instead of allowing them to proceed, police arrested all the demonstrators.
A BBC correspondent covering the protest was kicked to the floor by plain clothes security officers who seized his equipment.
The protest was organized after several Arab channels broadcast excerpts of a YouTube video showing blue-uniformed police officers taking turns whipping a young woman across her head, legs and feet.
Sudanese officials defended the whipping of women saying it is provided for in Islamic law.
However, they added the way this particular flogging was implemented is under investigation.