I'd like to suppress printing of a specific element on a page. I added a print media query to the page to hide a particular section of the page when printed. When I print from the browser, the section is now properly hidden. However Prince ignores the media query. Is there anything I can do to ensure Prince will listen to the print media query?

It should work, try this test document:

<style>
@media print {
    .hide { display: none }
}
</style>
<p>This will print.</p>
<p class="hide">This will not.</p>

I don't have access to Prince to do that directly, I can only print existing pages in our app. This is the code I inserted on the page:

@media print {
.approvals { display: none; }
}

Perhaps your app is specifying media screen?