Signs have been put up, with access for some being blocked in Buxton and Hayfield.
The authority added that some residents had been prevented from exercising in the area, and key workers have reported their route to work being inaccessible,with their cars being targeted with notes to stay at home.
Sarah Fowler, chief executive of the authority, told the BBC: "I can understand a reaction to the high numbers of visitors we saw last week could, for some, be seen as needing to set up makeshift closures and blockages to rights of way.
"However, this is unauthorised activity. There have been no changes to rights of way legislation as a result of the Covid-19 measures."
She added that any signs to say routes are closed are not from the authority.