This issue has been addressed in the recent version of Neovim (>=v0.2.2-dev) which you could use instead of Vim.
Once NVim v0.2.2 is released, you should be able to run:
$ echo foo | nvim -
without having the message.
For Vim, you need to use this custom patch proposed by @rdebath:
diff --git a/src/fileio.c b/src/fileio.c
index 87a46b1..939403b 100644
--- a/src/fileio.c
+++ b/src/fileio.c
@@ -825,7 +825,7 @@ readfile(
* still be running, don't move the cursor to the last line, unless
* always using the GUI.
*/
- if (read_stdin)
+ if (read_stdin && isatty(0))
{
#ifndef ALWAYS_USE_GUI
mch_msg(_("Vim: Reading from stdin...\n"));
So it's only displayed when user hasn't redirected stdin.