"\u" is a known escape sequence (meaning "uppercase"), so you need to write "\\u" or '\u' instead:

use Encode;
use strict;
use warnings;
use 5.010; # only required for say(), not for the encoding stuff

binmode STDOUT, ':encoding(UTF-8)';

$_ = "\\u6b63";
$_ =~ s/\\u(.{4})/chr(hex $1)/eg;

say $_;
[download]

See also: Perl and Unicode.