You can put that directly in your sites’ dashboard in the custom code tab, in the head section, in between style anchors:
<style>
/* Removes shadow on calendar popups BEGIN */
.ai1ec-modal-content { -webkit-box-shadow: none; box-shadow: none; }
/* Removes shadow on calendar popups END */
</styles>
Or you can put the same code anywhere in the calendar page in an HTML code widget.
The former will affect all the site, the latter only the calendar page.