In Moodle 3.1 (and maybe in previous versions too) the way to accomplish this within the user interface, was to:

1. Edit the 'student role' under: Site administration / ►Users / ►Permissions / ►Define roles

2. In the bottom of the page search for moodle/course:viewparticipants and click "Advanced options" to show all the options in buttons (not set, allow, prevent, prohibit ) within the capabilities.

3. Select the 'Prohibit' button

Under the navigation menu, the 'participants' link still shows and the students can see their own profile but they can't see other participants