Using Corion's HTTP::Request::FromCurl:

curl2lwp.pl  -H "Authorization: PASSWORD" -H "Content-Type: applicatio
+n/json" -d '{"message":"Test message"}'  https://myurl.url.url/api/v1
+/actions/message/

    my $ua = WWW::Mechanize->new();
    my $r  = HTTP::Request->new(
        'POST' => 'https://myurl.url.url/api/v1/actions/message/',
        [
            'Accept'         => '*/*',
            'Authorization'  => 'PASSWORD',
            'Host'           => 'myurl.url.url:443',
            'User-Agent'     => 'curl/7.55.1',
            'Content-Length' => '26',
            'Content-Type'   => 'application/json',
        ],
        '{"message":"Test message"}'
    );
    my $res = $ua->request( $r, );
[download]

Update: See https://corion.net/curl2lwp.psgi for an online version (Thanks Discipulus).