you should try that with a custom Nav Walker. Here is a code example how it should work.
I check if the menu item is a category link. If yes, there is another check -> category count.
If the category don't have any posts the link won't be passed to the html output.
class Menu_Category_Count extends Walker_Nav_Menu {
var $number = 1;
function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
$indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';
$class_names = $value = '';
$classes = empty( $item->classes ) ? array() : (array) $item->classes;
$classes[] = 'menu-item-' . $item->ID;
$class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
$class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';
$id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
$id = $id ? ' id="' . esc_attr( $id ) . '"' : '';
$output .= $indent . '<li' . $id . $value . $class_names .'>';
$atts = array();
$atts['title'] = ! empty( $item->attr_title ) ? $item->attr_title : '';
$atts['target'] = ! empty( $item->target ) ? $item->target : '';
$atts['rel'] = ! empty( $item->xfn ) ? $item->xfn : '';
$atts['href'] = ! empty( $item->url ) ? $item->url : '';
$atts = apply_filters( 'nav_menu_link_attributes', $atts, $item, $args );
$attributes = '';
foreach ( $atts as $attr => $value ) {
if ( ! empty( $value ) ) {
$value = ( 'href' === $attr ) ? esc_url( $value ) : esc_attr( $value );
$attributes .= ' ' . $attr . '="' . $value . '"';
}
}
// Get Category + Category Count
$have_posts = true;
if ($item->object == "category") {
$category = get_category($item->object_id);
// Does the category have any posts?
if ($category->category_count == 0) $have_posts = false;
}
if ($have_posts) {
$item_output = $args->before;
$item_output .= '<a'. $attributes .'>';
$item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
$item_output .= '</a>';
$item_output .= $args->after;
}
$output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
}
}
If you never dealed with a custom nav walker take a look at this tutorial at tutsplus.