Ubercart shipping API, get the package object with php to send the tracking number to the client as email
Are you managing to save the tracking number to the order? With a bit of preprocess magic you could probably get the number as a variable to the invoice template that already gets sent out.

EDIT:

Something like the below would work, that I did to get extra data displayed in an invoice. I did this in my theme, so replace that with your own theme name (and the other capitalised bits). 

    function [THEMENAME]_preprocess_uc_order(&amp;$variables) {
        $variables['tracking_number'] = 
           db_fetch_object(db_query("QUERY TO GET TRACKING NUMBER"))-&gt;COLUMNNAME;
    }


Then if you put uc_order.tpl.php (needed as a dummy file so your theme can override other templates) and your own custom template into your theme directory then you are able to reference it in the template with a simple call like print $tracking_number;