Follow the steps so that you can turn off comments on Facebook profile picture:
Start by opening the Facebook application and then log in to your profile if you haven’t logged in already.
Tap on the profile picture at the top left corner.
Open the profile picture and tap to view the profile picture.
At the top right corner of the screen, tap on 3-dots.
Choose edit privacy from the drop-down menu.
Tap on see more and choose only me.
With this, you can set profile picture privacy as it will be visible to you, and now others will
not be able to comments on it.