Untested, but adapting from the Codex example for filtering the post class… basically changing get_the_categories()
to get_the_terms
and accounting for the name of the Product Category taxonomy.
// add category nicenames to post class
function product_category_class($classes) {
global $post;
foreach((get_the_terms($post->ID, 'product_cat')) as $term)
$classes[] = $term->name;
return $classes;
}
add_filter('post_class', 'product_category_class');