Mugabe criticized Pastor Evan Mawarire accusing him of being "foreign sponsored," and called on him to leave the country.
The 92-year-old was speaking at a gathering of mourners at the funeral of Charles Utete, a senior government official who died Friday.
He said the protests were not part of Zimbabwean culture.
"That way of living is not in our country, it's not part of us, let them go to those who are sponsoring them," Mugabe said.
"You can't urge people to adopt...violent demonstrations as a way of solving grievances," he added.
Mugabe also branded Pastor Evan a fake and asked the crowd to "beware of these men of the cloth."
"Not all of them are true preachers of the Bible," he added.
A viral movement
Mawarire's #ThisFlag has gained momentum among Zimbabweans who have followed him on social media as he called on Mugabe's government to address a failing economy and respect human rights.
Mawarire was briefly arrested last week but the charges were swiftly dropped. His supporters flooded social media with the #freepastorevan campaign until he was released. A smiling Mawarire was later seen waving to hundreds of supporters outside the court before being whisked away by his family members.
"The government has completely failed to look after its citizenry, and failed to listen to demands of its citizenry," Mawarire told a local radio station during the #ZimShutdown2016 protests.
Zimbabwe's economy collapsed in 2009, leaving the Zimbabwean dollar worthless because of hyper-inflation. The country adopted a multicurrency system dominated by the U.S. dollar.