While anyone with a GitHub Enterprise account can edit a public repository's wiki by default, you can restrict edit permissions to only repository collaborators.

  1. In the top right corner of any page, click your username. highlighted username

  2. On your profile page, click the Repositories tab, then click the name of your repository. Repository tab

  3. In your repository's right sidebar, click Settings. Settings tab
  4. Under Features, unselect Restrict edits to collaborators only. Wiki restrict editing

Further reading