Turning off op amp for low power application high side or low side
You can control the op-amp power (1.2mA or so @5V) with an MCU GPIO and use the same signal to control a CD4053 to switch the high side of the divider (power it from +12/0V, it draws almost no current, 40nA typical at room temperature). 

The CD4053 can withstand 20V or so abs max, so if your 12V line has transients on it you should make sure they are clamped to less than 20V under all conditions.