Perl does not provide any facilities for this. There is no more relation between My::Package and My::Package::Class than there is between Foo and Bar (aside from the fact that builtins such as use and require, when asked to load My::Package::Class will look for Class.pm under subdirectories My/Package off the search path).

You could choose to live dangerously by messing with symbol tables:

use strict;
use warnings;

package My::Package::Class;

sub new {
  return bless +{};
}

sub foo {
  print "hello from " . __PACKAGE__ . "::foo\n";
}

package main;

*Class:: = \%My::Package::Class::;

my $object = Class->new();

$object->foo();
__END__
hello from My::Package::Class::foo
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but I think that such tricks would make your code confusing to anyone else but you.