Face coverings will become mandatory in libraries, museums and places of worship from Saturday.
Masks must currently be worn in shops and on public transport but a decision to expand the list of places was confirmed by the First Minister.
She said “risks are heightened” as the country eases lockdown measures.
Speaking at the daily coronavirus briefing, Sturgeon also said that, based on scientific advice, it wasn’t thought face visors provided sufficient protection.
As a result, from Saturday if a visor is worn it must be accompanied by another type of face covering.
The Scottish Government will make it mandatory for pubs and other venues to collect customer details from next Friday, Sturgeon added.
The requirement will be placed on a “statutory footing”, she said, and will help ensure test and protect can function as effectively as possible.
She also said the Scottish Government will issue new statutory guidance related to indoor hospitality to ensure greater compliance with coronavirus measures, to take effect from next Friday.
Police Scotland will enforce the measures if necessary.
The measures are introduced as a common factor in the rise in coronavirus outbreaks across the world, Sturgeon said, is a link to hospitality.
Confirmed coronavirus cases in Scotland have risen by 43 in the past 24 hours.
No patients have died after testing positive for the virus for 22 consecutive days.