Simple WordPress plugin that allow administrators to revoke access to profile to some users. Wrote to anwer a question on WPSE: http://wordpress.stackexchange.com/q/141743/35541

revoke-profile-access.php

<?php 
/**
 * Plugin Name: Revoke Profile Access
 * Description: Allow administrators to revoke access to profile to some users
 * Plugin URI: http://wordpress.stackexchange.com/q/141743/
 * Author: G. M.
 * Author URI: http://wordpress.stackexchange.com/users/35541/g-m
 * License: GPLv2
 *
 */
 
/*
  Copyright (C) 2014 Giuseppe Mazzapica

  This program is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License
  as published by the Free Software Foundation; either version 2
  of the License, or (at your option) any later version.

  This program is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 */

add_action( 'personal_options', 'rpa_profile_ban_field' );
add_action( 'edit_user_profile_update', 'rpa_profile_ban_field_save' );
add_action( 'admin_menu', 'rpa_profile_menu_remove' );
add_action( 'wp_before_admin_bar_render', 'rpa_profile_adminbar_remove' );
add_action( 'load-profile.php', 'rpa_profile_banned_check' );
add_action( 'load-index.php', 'rpa_profile_banned_msg' );
add_action( 'all_admin_notices', 'rpa_profile_banned_msg' );

function rpa_profile_ban_field( \WP_User $user ) {
  $current = wp_get_current_user();
  if ( ! is_admin() || $user->ID === $current->ID ) return;
  if ( ! user_can( $current, 'edit_users' ) ) return;
  $target = new WP_User( $user->ID ); 
  if ( $target->exists() &&  ! user_can( $target, 'edit_users' ) ) {
  	$banned = (int) get_user_meta( $user->ID, '_profile_banned', TRUE );
  ?>
  <table class="form-table"><tbody><tr>
  <th scope="row">Profile Ban</th><td>
  <input<?php checked( 1, $banned ); ?> name="_profile_banned" value="1" type="checkbox">
  Ban user to enter profile?
  </td></tr></tbody></table>
  <?php
  }
}

function rpa_profile_ban_field_save( $userid ) {
  $current = wp_get_current_user();
  if ( ! is_admin() || $user->ID === $current->ID ) return;
  if ( ! user_can( $current, 'edit_users' ) ) return;
  $target = new WP_User( $userid );
  if ( ! $target->exists() || user_can( $target, 'edit_users' ) ) return; 
  $ban = filter_input( INPUT_POST, '_profile_banned', FILTER_SANITIZE_NUMBER_INT );
  if ( (int) $ban > 0 ) {
  	update_user_meta( $userid, '_profile_banned', 1 );
  } elseif ( get_user_meta( $userid, '_profile_banned', TRUE ) ) {
  	delete_user_meta( $userid, '_profile_banned' );
  }
}

function rpa_profile_menu_remove(){
	$remove = get_user_meta( get_current_user_id(), '_profile_banned', TRUE );
  if ( ! current_user_can( 'edit_users' ) && (int) $remove > 0 ) {
  	remove_menu_page( 'profile.php' );
  } 
}
	
function rpa_profile_adminbar_remove() {
  $remove = get_user_meta( get_current_user_id(), '_profile_banned', TRUE );
  if ( (int) $remove !== 1 || current_user_can( 'edit_users' ) ) return;
  global $wp_admin_bar;
  $account = (array) $wp_admin_bar->get_node('my-account');
  $info = (array) $wp_admin_bar->get_node('user-info');
  $logout = (array) $wp_admin_bar->get_node('logout');
  $account['href'] = $info['href'] = '#';
  $wp_admin_bar->remove_node('my-account');
  $wp_admin_bar->remove_node('user-info');
  $wp_admin_bar->remove_node('edit-profile');
  $wp_admin_bar->remove_node('logout');
  $wp_admin_bar->add_node($account);
  $wp_admin_bar->add_node($info);
  $wp_admin_bar->add_node($logout);
}

function rpa_profile_banned_check() {
  $remove = get_user_meta( get_current_user_id(), '_profile_banned', TRUE );
  if ( (int) $remove === 1 && ! current_user_can( 'edit_users' ) ) {
  	wp_redirect( add_query_arg( array( 'pbanned' => 1), admin_url('index.php') ) );
  	exit();
  }
}

function rpa_profile_banned_msg() {
  if ( current_user_can( 'edit_users' ) ) return;
  static $show = false;
  if ( current_filter() === 'load-index.php' ) {
  	$msg = (int) filter_input( INPUT_GET, 'pbanned', FILTER_SANITIZE_NUMBER_INT);
  	$banned = (int) get_user_meta( get_current_user_id(), '_profile_banned', TRUE );
  	$show = ( $msg === $banned && $banned === 1 );    
  } elseif ( current_filter() === 'all_admin_notices' && $show ) {
  	echo '<div class="error"><p>Sorry, you are not allowed to edit your profile.</p></div>';
  }
}

Thank you very much G.M.! It was a great and perfect solution. I am using the Woocommerce plugin and I still have the problem of profile editing in the "my account" page.

Could you add something to the plugin to remove the "edit" link? I don't mind that the user can read his profile but don't allow to edit it.

Thanks again!

Apologies if this is a silly question, but where would this code go?

Gah. It WAS a silly question. Installed as plugin. Many thanks and apologies.