The incident happened in the Strathspey area on Saturday April 23.
Police said that a 63-year-old man has been arrested and charged in connection with the disturbance.
A report will be submitted to the Procurator Fiscal for possible prosecution over the allegations.
Constable Gary Dunlop of Aviemore Police Station said: “Capercaillie are extremely sensitive to disturbance which can seriously hamper their breeding success.
“All reports and information received regarding possible disturbance at lekking sites, will be taken very seriously.”
The capercaillie became extinct in the UK in the late 18th century but was reintroduced successfully to Scotland in the middle of the 19th century.
Conservationists say it is likely that there are now fewer than 1,000 capercaillie left in the UK and almost all of them are found in the Cairngorms National Park.
Due to their vulnerable status, capercaillie are listed as a Schedule 1 species of the Wildlife & Countryside Act 1981. This makes it an offence to intentionally or recklessly disturb a capercaillie whilst it is lekking. It is also an offence to: Disturb capercaillie whilst they are nest building at or near a nest with eggs or young, to obstruct or prevent a capercaillie from using its nest and to amage, destroy or interfere with a capercaillie nest while it’s in use or being built.
It is also an offence to disturb the dependent young of a capercaillie, kill, injure or take a capercaillie and to take or destroy their eggs.