The moves come as cases of the disease in the country rise and Nigerians flout preventive measures.
According to the order, which was signed on January 27, all Nigerians should wear face masks at all gatherings and keep a physical distance of at least two metres.
Public places include open markets, malls, supermarkets, shops, restaurants, hotels, event centres, gardens, leisure parks, recreation centres, motor parks and fitness centres.
According to the order, no person shall be allowed within these places without a face covering that covers the nose and mouth, washing of hands or cleaning them using hand sanitiser approved by the Agency for Food and Drug Administration and Control, and checking of body temperature.
Failure to wear a face mask in public attracts a six-month prison sentence.
The country now has 127,024 confirmed Covid-19 cases, according to the Nigeria Centre for Disease Control.
Africa’s biggest economy continues to fight a surge in cases as it records more than a thousand cases daily now in the second wave of the Covid-19 pandemic.