Hide other shipping methods when FREE SHIPPING is available

BEFORE and AFTER adding the snippets, make sure you clear your WooCommerce cache (WooCommerce → System Status → Tools → WC Transients → Clear transients), as shipping methods are cached.

/**
 * Hide shipping rates when free shipping is available.
 * Updated to support WooCommerce 2.6 Shipping Zones.
 *
 * @param array $rates Array of rates found for the package.
 * @return array
 */
function my_hide_shipping_when_free_is_available( $rates ) {
  $free = array();
  foreach ( $rates as $rate_id => $rate ) {
    if ( 'free_shipping' === $rate->method_id ) {
      $free[ $rate_id ] = $rate;
      break;
    }
  }
  return ! empty( $free ) ? $free : $rates;
}
add_filter( 'woocommerce_package_rates', 'my_hide_shipping_when_free_is_available', 100 );

Source: https://docs.woothemes.com/document/hide-other-shipping-methods-when-free-shipping-is-available/