Can an Arduino power itself off [not low power mode] via software?
In general, an Arduino by itself has no control over its power input.  It can, of course, enter various Sleep modes, such as the Power-down mode with watch-dog-timer off, which uses 0.1  μA.

It isn't clear from the question what will turn the Arduino back on after it is off for a while, but if you have either a push-button or a signal to turn it back on, the Pololu 2808 Mini Pushbutton Power Switch will work as an Arduino-controlled off switch.  This board has On, Off, Ctrl, and button-contacts inputs.  If your Arduino raises the Off input, power shuts off cleanly.  To turn it back on, either connect the  button-contacts inputs together, or raise the On input, or pulse the Ctrl input.