Since the military deposed Morsi on July 3 last year, the authorities have waged a brutal crackdown on his supporters that has seen more than 1,400 people killed in street clashes and over 15,000 jailed.
Magdy Hussein, a leader of the Anti-Coup Alliance that has spearheaded protests demanding Morsi's reinstatement, was arrested at dawn at his house, the security officials said.
He faces charges of inciting violence and threatening national security and stability.
Two other leaders of the party were also arrested.
More From This Section
The Anti-Coup Alliance condemned the arrests as "kidnappings" and renewed its call for pro-Morsi protests during a "day of rage" on Thursday, marking the first anniversary of his ouster.
Former army chief Abdel Fattah al-Sisi led the ouster of Morsi after millions rallied against the Islamist's divisive one-year rule.
Sisi himself became Egypt's president after winning a May election in a landslide.
Hundreds of Morsi supporters have already been sentenced to death after speedy trials.