You want, essentially, the current consumption of the ATmega168 chip itself, since that's about the only power-consuming chip ON the mini. You can get a rough idea from the Atmel Atmega168 data sheet. This is in the form of a "maximum" power consumption in the "DC characteristics section" (page 301: 12mA @ 8MHz) that you have to extrapolate to 16MHz (current consumption is pretty linear vs frequency.) Or you can look at the "typical" "Active Supply current vs Frequency" graph (page 309: Looks like about 9mA at 16MHz.)
That gives you a pretty broad ranges of estimates (less than 9 to about 24 mA)... Next you get to test and measure...