Town and parish councils have closed public toilets at Ironbridge Gorge, Newport, Madeley, Dawley and Wellington.
Telford & Wrekin Council has shut its play areas, and the Southwater multi-storey car park will also be closing from today.
The closures will remain in force until further notice.
Telford & Wrekin Council spokesman Russell Griffin said: "These closures are to help stress to people the importance of social distancing as set out by the Government and help to reduce the spread of coronavirus.
"Parks and green spaces are still accessible so that people can exercise, however it is vital that people follow the Government’s guidance and stay at least two metres apart.
"Please do not congregate in large groups.
"You should be staying in your homes as much as you can and avoid social contact wherever possible.
"We will keep this under review, particularly if people do not follow social distancing advice."