Face coverings will be mandatory on all public transport from Monday.
Under fives and people with breathing difficulties will be exempt.
Passengers in taxis, trains buses and the Glasgow Subway must wear a face mask or covering to be allowed to travel.
Ms Sturgeon said it can reduce the risk of the virus being transmitted.
She said the Government was also consulting on whether it should be compulsory in shops when non-essential retail is allowed to open later this month.
Nicola Sturgeon announced the rule as she revealed the latest changes to easing lockdown
The phase two changes will be introduced gradually ove the next three weeks.
It means people who live alone can form an extended group with another household, meaning a grandparent can have family to stay.
Ms Sturgeon revealed from tomorrow, people who live alone or with children under 18 can have a bubble with one other household. She said you can visit indoors and stay overnight but it has to be with this household only.
It means people who live alone can meet up with someone else indoors and overnight without physical distancing.
Starting tomorrow people can meet outdoors with up to 2 other households but still no more than 8 people.
The First Minister said you can also go indoors, where necessary, to use the toilets etc.
Dentists can reopen for emergence work only and professional sport canresume behind closed doors.
From Monday indoor workplaces can re-open including factories, warehouses and laboratories.
Playgorunds can open and outdoor sports centers and zoos will be allowed to open.
Non essential retail will re-open from June 29 but only those with an outdoor entrance and exit.
It means shopping malls like St Enoch and Buchanan Galleries will need to wait longer before they can open.
Ms Sturgeon also said that the evidence on outdoor beer gardens is still hat they can be hostspots for transmission.
She said that she will set out more information on July 2. Ms Sturgeon said that: “We need to understand this before we allow re-opening.”
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