Zimbabwe's President Emmerson Mnangagwa on Tuesday threatened 20 years in jail to the author of a statement purporting to bear his signature that said the lockdown to contain the coronavirus outbreak had been extended.

Mnangagwa, who was speaking at his farm after touring Gweru city in central Zimbabwe, told state broadcaster ZBC the statement, which circulated on social media last week and was immediately denied by the government, was fake.

"That is absolutely nonsense, I have never made such a statement," Mnangagwa said.

"If we catch this person it must be exemplary and they must go in for at least at level 14, which is 20 years imprisonment. That, I think we need to demonstrate that we don't want false news to be circulated."

Zimbabwe last month published lockdown regulations, which included jail terms of up to 20 years for people who spread falsehoods regarding the outbreak.

National police spokesperson Paul Nyathi said more than 5,000 people had been arrested for venturing outside their homes without permission.