If you mean the Message-Id header, you should be able to retrieve it like any other header. I use MAIL::IMAPClient in one of my scripts. Here's an example, taken from my code:

# ($imap is a MAIL::IMAPClient object already connected to the server)

$imap->Uid(0);
$imap->select('INBOX');
$totalMessages = $imap->message_count();
for my $messageSequenceNumber (1 .. $totalMessages)
{
    my @headerList = ('Message-ID', 'From', 'Subject', 'To', 'Date');
    my $headers = $imap->parse_headers($readMessage, @headerList);
    print "Message-Id is --> $$headers{'Message-ID'}[0])";
}
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However, if you're already using other modules I'm sure you can get the value using them. Search the docs to see how to retrieve a specific header's value.