Step 1. Log in as an administrator and select Administration
Step 2. Select Site Administration
Step 3. Select the Users tab
Step 4. Scroll down and find the Permissions category
Step 5. Select Define roles
Step 6. From the list, select the user role for which you’d like to remove the ability to edit their user profile.
Please note - If you select Authenticated user, this will remove the ability for all users, including administrators and teachers to edit their user profile.
Step 7. For the chosen user role, select the COG icon in the same row as the user role, located under the Edit column.
Step 8. Scroll down to find the following capability, Edit Own user profile (String: moodle/user:editownprofile
Step 9. Select the checkbox that currently contains a tick. This will remove the tick and disable the ability for the user to be able to edit their own user profile.
Enabled (users can edit their own profile) -
Disabled (users cannot edit their own profile) -
Step 10. Scroll to the bottom of the page and select Save Changes. 
Users that have been assigned to this role, will no longer be able to edit their own profile field.