#Assuming $sth has just been executed with a "show tables" query
while(@tmp = $sth->fetchrow_array())
{
    my $tablename = $tmp[0];
    my $sth2 = $dbh->prepare("select count(*) from $tablename");
    $sth2->execute();
    $numrows = ($sth2->fetchrow_array())[0];
    if($numrows > 0)
    {
        push @tables, $tablename;
    }
}