People are being asked to follow government guidelines and only visit Burnham Beeches if they live locally.
The City of London Corporation, which manages the site, issued the call after visitor numbers tripled since March 2020, causing damage to the beauty spot.
The authority says the huge rise in visitor numbers is harming sensitive habitats, and concerns are growing that permanent damage will be done unless action is taken.
The wet winter conditions have made the situation worse.
Burnham Beeches is temporarily closing half its car parks from 1 February to help protect the European Special Area of Conservation and National Nature Reserve.
And Buckinghamshire Council is introducing parking restrictions on local roads to discourage casual parking on the highways and to ensure the safety of local residents.
Government guidelines say you can only exercise alone, with your household (or support bubble) or one other person (in which case you should stay 2m apart).
Exercise should be limited to once per day, and you should not travel outside your local area.
Chairman of the City’s City Commons Committee, Graeme Doshi-Smith, said: “Visits to this wonderful National Nature Reserve have risen from around 500,000 a year to nearly two million.
“This increase is sadly having a detrimental impact on the ground, and much of the damage could take decades to restore.
“We ask that people please remember the government guidelines and only visit if you live locally.
“With support we can all play our part in helping to protect Burnham Beeches. Please help us to protect this amazing protected site.”
The City Corporation has updated signage at its open spaces in line with the latest government guidance.
Social distancing should be maintained when around other people. Further information is available here.
Burnham Beeches was bought by the City of London Corporation in 1880 to protect it as a public open space and wildlife reserve.
It has been a Site of Special Scientific Interest (SSSI) since 1951, was declared a National Nature Reserve in 1993 and designated as a Special Area of Conservation in 2005.
Burnham Beeches is characterised by a diverse mixture of ancient woodland, wood pasture, coppice, ponds and streams, grassland, mire and heathland.
The City Corporation owns and manages 11,000 acres of green space in London and south east England – including Hampstead Heath, Epping Forest and Burnham Beeches – and over 200 smaller ones in the Square Mile.