The interior ministry said the demonstration organised by activist groups would be held at Talaat al-Harb Square in downtown Cairo later today.
The first to win official approval since the disputed law on demonstrations was adopted on Sunday, the rally would also demand the release of detained protesters.
Last day, police arrested dozens of people as they broke up protests by youth movements and activists against the law that bans demonstrations held without prior notice.
The new law requires protest organisers to apply to the ministry for permission to hold any demonstrations at least three days before they are staged.
The disputed law says protesters can be jailed for up to five years if found guilty of offences ranging from covering their faces to carrying weapons during demonstrations.
It also says security forces must first verbally warn protesters at prohibited demonstrations to disperse before using water cannon or tear gas, and should only gradually escalate to the firing of birdshot if other means fail.