The case was the first time a private citizen has asked the court to decide whether actions by 92-year-old Mugabe, the world's oldest leader, violated the constitution.
Mugabe, who has ruled the former British colony since independence in 1980, was last year confronted by the biggest anti-government protests in a decade. Security forces responded with teargas and water cannon.
Political activist Promise Mkwananzi, whose #Tajamuka group helped organise the demonstrations, said in his application that Mugabe's response and speeches in the protests' aftermath "undermined national security and threatened citizens."
At a meeting with war veterans after one of the protests, Mugabe said his ruling ZANU-PF punished defectors during the liberation war by keeping them "underground like rats, in bunkers" - something he threatened to do to protest leaders.
Mkwananzi said Mugabe also claimed partisan control of the police and army, which is against the constitution.
