If I read you correctly, what you want is something like this:

my $mod_ref;
my %modules;
while (<CONFIG>) {
   chomp;
   my $mod_name =$_;
   my $mod_ref = My::Base::Class -> new($mod);
   $modules{$mod_name} = $mod_ref;
}
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Note: Untested, just off the top of the (only slightly caffeinated as yet) head.

Use the new() method of your base class as a Factory Object to build references to your sub-modules. Each (blessed) reference gets saved in %modules for later use. If you are feeling appropriately paranoid, you wrap this in an eval.