Example page source:
PROBLEM:
I was having the same issue. Sizing/styling the iframe's container div and adding scrolling="no" to the iframe didn't work for me. Having a scrolling overflow like Freya describes wasn't an option, either, because the contents of my iframe needed to size depending on the parent container. Here's how my original (not working, overflowing its container) iframe code was structured:
SOLUTION:
This super simple little CSS hack did the trick:
Set the iframe's height/width to some small, random pixel value. Set it's min-height & min-width to what you actually want the height/width to be. This completely fixed the issue for me.