Moroccans, who venture outside their homes without wearing face masks, risk prison sentences of up to three months and a fine of up to $126 (£102).
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The new order takes effect on Tuesday for those leaving their homes during the coronavirus lockdown, which began in mid-March.
The decision was announced on Monday after a government meeting about how to control the spread of the virus.
Face masks are to be sold at a subsidised price of $0.08 each.
By next week, Morocco plans to be producing almost six million face masks a day, an increase from the current figure of 3.3 million, industry ministry spokesman Taoufiq Moucharraf told the Reuters news agency.
The North African nation has so far reported 1,141 coronavirus cases and 83 deaths.
It imposed a month-long public health state of emergency on 19 March. People can leave their homes to buy food or medicine – but only those with permits can go to work.
Since then, more than 8,600 people have been arrested and prosecuted for flouting lockdown rules, including failing to produce a permit, illegally transporting people, or selling counterfeit goods, according to an official report quoted by Le Figaro newspaper.
At the moment the World Health Organisation (WHO) does not recommend face masks to be worn by the general public, advising them for the sick or those caring for patients with coronavirus.
It says frequent hand-washing and social distancing are more effective at stopping the spread of the virus, but a WHO panel is assessing further research on the matter.
Experts warn that face masks must be worn correctly, changed frequently, removed and disposed of properly and be used in combination with good hygiene.
Over the weekend, Americans were advised to use clean cloth or fabric to cover their faces whilst in public.
European advisers say reusable cloth masks may increase the chance of infection as there is a high chance virus particles could go through cloth and problems with moisture could also mean the cloth retains the virus.