WooCommerce Hide shipping costs when Free Shipping is activated

This can be achieved using Table Rate Shipping or a code snippet like shown below. These code snippets can be added to your theme/child-theme’s functions.php file. Before adding the snippets, make sure you clear your WooCommerce cache (WooCommerce > System Status > Tools > WC Transients > Clear transients), as shipping methods are cached.

Snippets for WC 2.6+

/**
 * 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 );

Snippets for WC 2.5

/**
 * woocommerce_package_rates is a 2.1+ hook
 */
add_filter( 'woocommerce_package_rates', 'hide_shipping_when_free_is_available', 10, 2 );
 
/**
 * Hide shipping rates when free shipping is available
 *
 * @param array $rates Array of rates found for the package
 * @param array $package The package array/object being shipped
 * @return array of modified rates
 */
function hide_shipping_when_free_is_available( $rates, $package ) {
 	
 	// Only modify rates if free_shipping is present
  	if ( isset( $rates['free_shipping'] ) ) {
  	
  		// To unset a single rate/method, do the following. This example unsets flat_rate shipping
  		unset( $rates['flat_rate'] );
  		
  		// To unset all methods except for free_shipping, do the following
  		$free_shipping          = $rates['free_shipping'];
  		$rates                  = array();
  		$rates['free_shipping'] = $free_shipping;
	}
	
	return $rates;
}