Yes make the profile-photo post Only Me so it won’t notify others. On the Facebook app: go to Profile → Edit Profile → Add/Change Profile Photo, choose the photo, tap the audience selector (people icon) and pick Only Me, then Save. On desktop: click your profile photo → Update Profile Photo → Upload Photo, set the post audience to Only Me, and save.
If you already changed it publicly, delete the profile-photo post or change its audience to Only Me to remove the notification.