• Putting the code in VERSION makes it less useful.
• Gave function a prototype that will allow user to omit quotes around module name.
• The module name was both a parameter and hardcoded. Removed the hardcoding.
• Broke infinite loop if version not found.
• Don't try to load twice from the same @INC path.
• Made strict-safe and warning-safe.

use Carp qw( croak );

sub require_exact_ver(*$) {
   my ($pkg, $desired_ver) = @_;

   {
      my $ver = $pkg->VERSION;
      return 1 if defined($ver)
               && $ver == $desired_ver;
   }

   my $file = $pkg;
   $file =~ s{::}{/}g;
   $file .= '.pm';

   foreach $inc (@INC) {
      delete $INC{$file};
      local @INC = $inc;
      eval { require $file }
         or next;

      my $ver = $pkg->VERSION;
      return 1 if defined($ver)
               && $ver == $desired_ver;
   }

   delete $INC{$file};
   croak("Unable to load $pkg version $desired_ver");
}
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You might get lots of redefined warnings. Other hard to debug problems might also surface. To avoid those, you might want to take CPAN's approach to determining a module's version. CPAN searches for $VERSION in the source and executes only that line (more or less). Since the module isn't actually loaded, no redefined problems, etc.

use Carp       qw( croak );
use File::Spec qw( );

sub require_exact_ver(*$) {
   my ($pkg, $desired_ver) = @_;

   my $file = $pkg;
   $file =~ s{::}{/}g;
   $file .= '.pm';

   if ($INC{$file}) {
      # Module already loaded.

      my $ver = $pkg->VERSION;
      return 1 if defined($ver)
               && $ver == $desired_ver;

      croak("$pkg version $ver already loaded (want $desired_ver)");
   }

   local $/;

   foreach $inc (@INC) {
      next if ref($inc);  # XXX

      my $path = File::Spec->catfile($inc, $file);

      open(my $fh, '<', $path)                          or next;
      my $file = <$fh>                                  or next;
      my ($ver_cmd) = $file =~ /\$VERSION\s*=([^\n;]);/ or next;
      my $ver = eval $ver_cmd                           or next;
      $ver != $desired_ver                              or next;

      # woot!
      require $path;
   }

   croak("Unable to locate $pkg version $desired_ver");
}
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