Positioning of the IconButton as an InputAdornment should be the same on IE11 as it is on other browsers.
The IconButton is rendered too low and further to the right (for a right adornment).

The horizontal positioning issue can also be seen on the example on material-ui-next.com. However, the vertical positioning seems to come from using an IconButton.
The horizontal issue is because width: 100% is set on the input element. Removing this and setting flex-grow: 1 fixes this.
The vertical issue can be fixed by setting a fixed height of 48px on the input adornment.
| Tech | Version |
|--------------|---------|
| Material-UI | 1.0.0-beta.33 |
| React | 16.2.0 |
| browser | IE11 |
| etc | |
It's working on Material-UI side on IE 11. I'm not sure I can help. Maybe it's a JSS issue?

Even there, it's right up against the right hand edge of the text field, whereas on chrome there is more padding:

The vertical difference is a bigger issue, and seems to be from using a material-ui/Icon rather than something from material-ui-icons?
Oops, this issue hasn't be resolved.
Ok, so the documentation issue with IE11 was solved. Now I can confirm that it's working fine with IE11 with the server side generated CSS and with the client side generated CSS.
IE 11

on beta.41 IE11 renders as follows:

seems to be broken again to me
@FranBran It renders correctly on my end (v1.0.0-beta.41):



@oliviertassinari Your screenshot shows the password field adornment in the wrong place - it isn't inside the field.
I find that adding width: 100% to the HTML input element fix this.
See sandbox https://codesandbox.io/s/zqz6nyxvr3
Screen shot in IE 11:

Most helpful comment
I find that adding
width: 100%to the HTML input element fix this.See sandbox https://codesandbox.io/s/zqz6nyxvr3
Screen shot in IE 11: