The southern African nation last month published lockdown regulations, which included jail terms of up to 20 years for people who spread falsehoods regarding the outbreak.
National police spokesman Paul Nyathi said more than 5,000 people had been arrested for venturing outside their homes without permission.
Mnangagwa said his cabinet would meet this week to decide whether to end, adjust or extend the 21-day lockdown.
The authorities have said three people have died and 17 people have been infected in the country of 15 million people. Just over 600 people had been tested by Monday night.
In the past week, Zimbabwe has deployed the army to help the police enforce the restrictions.
The Zimbabwe Lawyers for Human Rights (ZLHR) group said this had resulted in an increase in cases of residents being beaten by security forces for defying the lockdown.
Police spokesman Nyathi said police had not received any official complains of abuse from residents.
ZLHR has approached the High Court on behalf of two Zimbabweans who said they were abused by security forces.
"This application seeks an order to protect residents from heavy-handed action by police and soldiers who are invading peoples homes/yards and assaulting people ordering them to stay indoors," ZLHR said in a statement.
Zimbabwe's security forces have a history of using heavy handed tactics when enforcing the law and against opponents of the government.
In an editorial on Monday, the state-owned Herald newspaper criticised the police for harassing journalists doing their work during the lockdown, including forcing some to delete pictures and video that captured abuses by security forces.
Nyathi said he was not aware of the incidents.
Reuters