Ahmed Douma, a blogger and activist who has called for Mursi's trial over the shooting deaths of protesters, was ordered held for four days by prosecutors in the Nile Delta city of Tanta, lawyer Ali Soliman told AFP.
The prosecutors were investigating a complaint accusing Douma of insulting Mursi, filed by a member of Morsi's Freedom and Justice Party, Soliman said. He said Douma turned himself in yesterday.
Mursi, elected last June, has been accused of cracking down on opposition and critical journalists.
The state prosecutor last month opened a new investigation into television satirist Bassem Youssef on suspicion of "threatening public security."
Youssef, who regularly skewers the country's ruling Islamists on his wildly popular show, was released on $2,200 bail after an interrogation that lasted nearly five hours.
Since taking office, Mursi has faced waves of sometimes deadly unrest led by a loose coalition of secular leaning parties and youth protest movements that helped oust president Hosni Mubarak in 2011.
The Muslim Brotherhood, on whose ticket Mursi ran in the election, had filed a complaint against Douma among other activists, accusing him of inciting violent clashes outside its headquarters in March.
