Be aware that you are wandering into a bit of a quagmire.
Not an impossible one, but there are a few things to be aware of, as the power situation for MC's is a little different than other Atari raster games. And the details of such are not well documented, or aware to a lot of folks. Even I don't have all of the info, but I've researched this a bit, and can tell you what I know. We can start with this chart:
http://www.elektronforge.com/transassy.htm
However, that chart doesn't tell the full story, as there were four kinds of MC cab. Upright, cabaret, cocktail, and cockpit. (Yes, cockpit.) And they each used slightly different power schemes.
MC *uprights* originally came with a brick that is different that the typical type of Atari raster brick. It's referred to as a 'Type B' brick, and you can see one on page 31 of the manual (TM-147, 3rd Printing), here:
http://www.gamesdatabase.org/Media/SYSTEM/Arcade//Manual/formated/Missile_Command_-_1980_-_Atari.pdf
(here's the pic from the manual)
I *believe* based on the schematics (DP-147, 2nd Printing, below), that this brick outputs 115V, so it can be used with normal 120V monitors.
http://arcarc.xmission.com/PDF_Arcade_Atari_Kee/Missile_Command/Missile_Command_DP-147-2nd-01A.pdf
Note this brick is also the same one used in older Atari b/w raster games, per this thread:
http://www.jammaplus.co.uk/forum/forum_posts.asp?TID=45854&title=missile-command-schematics-anyone
The CABARET used a 100V monitor, which required another special brick, and I believe is the one listed in the Elektronforge table above, but not 100% positive. I have one of these bricks, and it physically looks like the other Atari bricks, but is NOT the same as a Pole Position or Centipede brick (which are the same, as all other Atari color raster games used/use the same brick.)
From the schematics, it looks like this brick can put out 100 and 120V, on different pins.
Again, I don't have all of the details for everything. But bottom line, be aware there are different bricks, with different voltages, and they likely have different pinouts as well, for different harnesses. You can use a standard 120V monitor, but you will need to be sure you have a 120V brick for it, and in that case the harness you have may or may not be compatible. So you will need to measure and triplecheck everything before applying power.
Also, a Centipede harness will not work natively, as MC has more buttons than a Centipede CP, and likely a different edge connector pinout. However, Centipede was set up for a 120V monitor, and a 120V standard raster brick, so you conceivably could get a Centipede harness, extract and re-organize the pinout of the edge connector, and add whatever wires may be needed for the extra buttons on the MC CP. That arguably might be a reasonable option, if you can't find a complete original brick, harness, and compatible monitor.