Under Phase 3 of the Scottish Government’s roadmap out of lockdown, cinemas, monuments and libraries can also begin to reopen.
Visitors are expected to observe physical distancing and with this in mind advance booking will be required at many locations.
Government guidance to venues calls for various measures including strict physical distancing, enhanced hygiene, staff training and advice for customers.
This comes at the same time as tourism and hospitality businesses such as hotels, cafes, restaurants and bars open their doors to allow patrons indoors.
Culture secretary Fiona Hyslop said: “We have made major progress in tackling coronavirus (Covid-19) and prevalence of the virus in Scotland continues to be lower than it is across the UK as a whole.
“It is because of this that we can continue to take these steps out of lockdown and start to safely welcome visitors back to our museums, galleries, and other attractions across the country.
“This is a positive step forward for cultural venues and visitor attractions, which have been hit hard by the pandemic.
“Our guidance, developed in partnership with employers, industry bodies and trades unions, provides the information these venues need to ensure the safety of staff and customers as they begin to re-open, and can give confidence to those who want to visit them.
“Museums and galleries play a crucial role in our communities and I’m sure that many people, including tourists, will be looking forward to our cultural sites and heritage spaces opening up again.
“If everyone sticks to the rules we will be able to drive the virus down further and live less restricted lives in the weeks and months ahead.
“People should look for those safety measures and be aware of the need to follow the FACTS at all times when out in the community.”