WooCommerce - get category for product page

$product->get_categories() is deprecated since version 3.0! Use wc_get_product_category_list instead.

https://docs.woocommerce.com/wc-apidocs/function-wc_get_product_category_list.html

A WC product may belong to none, one or more WC categories. Supposing you just want to get one WC category id.

global $post;
$terms = get_the_terms( $post->ID, 'product_cat' );
foreach ($terms as $term) {
    $product_cat_id = $term->term_id;
    break;
}

Please look into the meta.php file in the "templates/single-product/" folder of the WooCommerce plugin.

<?php echo $product->get_categories( ', ', '<span class="posted_in">' . _n( 'Category:', 'Categories:', sizeof( get_the_terms( $post->ID, 'product_cat' ) ), 'woocommerce' ) . ' ', '.</span>' ); ?>