Please read perlre to learn how to escape strings. You will likely want to use quotemeta respectively the \Q...\E string escapes to escape regex-special characters from your search string:

use strict;
use File::Find;

$file = 'test$file.class'; # note that you need to use single quotes h
+ere
find( sub { /\Q$file\E/ && print "$File::Find::name\n", $destDir });
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