Yes, but you have to call it a little differently.

	package Whatever;
	my $privatesub = 
	  sub { 
	    # blah blah blah 
	  };

	sub publicsub {
	  $privatesub->(arguments...);
	}

Here we've made an anonymous subroutine and stored it in a private my variable. No code outside this file will be able to see the $privatesub variable, so the private subroutine is only accessible from inside the file.

Since $privatesub is actually a reference to our private subroutine, we need to use the -> notation to invoke it.