Simple method (brute force):

#!/usr/bin/env perl 
use strict;
use warnings;

my @files = (
'000001.OrderID.html',
'000002.OrderID.cgi',
'000004.OrderID.js',
'000005.OrderID.txt',
'000006.OrderID.cgi',
'OrderID.master'
);

my $i = 1;
for my $infile (sort grep /^\d{6}\./, @files) {
    my $repl = sprintf ("%6.6i", $i++);
    (my $outfile = $infile) =~ s/^\d{6}/$repl/;
    rename $infile, $outfile;
}
[download]

You can replace the initial set-up of @files with a glob.

Update: comma was absent from penultimate line.

Thanks hippo for looking at this.

 push (@renamefiles, $outfile);

Indeed I can see the files renamed now, but 'OrderID.master' file is skipped, I need this file also in my @renamefiles array and name 'OrderID.master'should remain as is

Also, Instead of pushing the files to @renamefiles , can I do this change in same array @files and check the file name changed in @files array

Thanks again for your help.

This is a new feature - there was no mention of it in your original post. So, instead of re-engineering the solution already provided, you can just populate your @renamefiles array with a fresh glob after the renames have completed.