Putting the iframe in a appropriately sized div with overflow set to hidden resolved this issue - although this is only actually hiding the problem as such.
I couldn't get the display: none option to work with the HTML 5 version of the button. Instead I targeted the div that the like button button is created in and set the overflow to hidden.
Dropping the following in my main css file did the trick:
Agree with BrynJ, best solution currently is to put the like button in a 20px high div container, and set the overflow to hidden (I read somewhere that FB recently moved the comment flyout into the iFrame, so the solution that modifies the styling of .fb_edge_widget_with_comment is probably not useful anymore for iFrame users).
If you use the newer HTML5 button, and you should as it's forward compatible and suggested by Facebook, it's easy, going off from what others have said:
.fb-like, .addthis_button_facebook_like
height: 25px
overflow: hidden
The second class is a bonus for those using the AddThis plugin.
Change the 'URL to Like' to your Facebook page URL
Select any other options (Layout, Action Type, etc) as desired
Press the 'Get Code' button
Select the IFRAME version
Make sure you select your Facebook application where it says 'This script uses the app ID of your app'
Implement the provided code in your application
From what I can see, the like button with IFRAME implementation does not trigger any pop-up. It simply functions as a like button. This was my desired outcome.