How to bind click event to object tag?

The easiest way to accomplish this goal is to wrap the object tag in a div, bind the click listener to the div, and add pointer-events: none to the object tag's styles.

Sample fiddle:

.clickable {
  background: red;
  width: 100px;
  height: 100px;
  border-radius: 100px;
  overflow: hidden;
}

object {
  width: 100%;
  pointer-events: none;
}
<div class='clickable' onclick='alert("WOW")'>
  <object type='image/svg+xml' data='https://douglasduhaime.com/assets/images/icons/home.svg' />
</div>

1. Issue: Event handling

Concerning the jQuery part, try to use event delegation.

From the docs:

The .on() method attaches event handlers to the currently selected set of elements in the jQuery object.

$(document).on('click', '.icon-logo', function(event) {
    document.write('Event type: ' + event.type);
    document.write('<br>CSS-Class: ');
    document.write($(this).attr('class'));
});
// As said in the docs, you can attach multiple events to multiple selectors. 
// A typical example of use may be:
// $(document).on('change blur', '.icon-logo .some-other-class', function() {...}
 
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<object data="images/logo.svg" type="image/svg+xml" class="icon-logo" style="cursor: pointer;">Click me!</object>

Edit after @Kaiido's comment:

2. Issue: The <object> element can't be clicked.

One possibility could be to not use an <object> at all but an <img> tag instead as suggested in this SO answer: make an html svg object also a clickable link.


2. Issue: Empty HTML-tag

This kind of tag <object> needs some content to show up on the page.

Your tag:

<object data="images/logo.svg" type="image/svg+xml" class="icon-logo"></object>

is not having any inner HTML-Content, so you won't be able to click it.