"The president is well and in very good health," Osama Morsi told The Anadolu Agency on Monday.
A post was earlier published on the Morsi family's Facebook page that the ousted president had died.
"This report was totally groundless," Osama said, adding that the Facebook page had been "hacked."
"Until we reestablish control of the page, whatever is published does not represent us," he said.
Morsi, Egypt's first democratically elected leader, was ousted by the military in mid-2013 – after only one year in office – following opposition protests against his presidency.
He currently faces separate trials on multiple criminal charges, including espionage, jailbreak and "offending the judiciary."
Morsi, like all of his co-defendants, insists that the charges are politically motivated.