Mnangagwa’s warning was issued following violent protests last month during which, some reports say, 17 people were killed.
Six people were killed in August last year following demonstrations that turned violent.
The United States and the European Union have accused Zimbabwe’s security forces of using unwarranted force to deal with the demonstrations and the EU is threatening to impose stiffer sanctions on Zimbabwe.
Mnangagwa said demonstrations are constitutional as long as they are peaceful.
He, however, warned those intending to hold violent protests that the security forces will deal with them.
He said after 20 years under sanctions Zimbabwe has decided to forge ahead despite the sanctions, which was seen as a clear indication that he was brushing off threats to impose stiffer sanctions by the EU and the United States.