Response code 307 was added to HTTP/1.1 to do just that. A 307 should redirect a POST, but whether clients recognize and obey this directive is unknown. Also, the RFC specifies that POST redirections require user intervention:

If the 307 status code is received in response to a request other than GET or HEAD, the user agent MUST NOT automatically redirect the request unless it can be confirmed by the user, since this might change the conditions under which the request was issued.

However, you are able to fake it. You can output an HTML form with hidden fields and ask the user to click the submit button. You might even be able to get JavaScript to click the button automatically.