[General Snippets][Hide other shipping methods when “Free Shipping” is available] Hides all other shipping methods but free_shipping if it’s available. Compatible with Shipping zones.

wc-hide-all-shipping-if-free-shipping-is-available.php

/**
 * 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 );

For purposes of facilitating copy and paste, here is the code from @JoyMovil above, but then properly formatted:

/**
 * Hide shipping rates when free shipping is available.
 * Updated to support WooCommerce 2.6 Shipping Zones.
 * 
 * Change `my_` part of function-name to something unique to your own site
 *
 * @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;
}

$package['rates'] = apply_filters( 'woocommerce_package_rates', $package['rates'], $package );

add_filter( 'woocommerce_package_rates', 'my_hide_shipping_when_free_is_available', 100, 2 );