How to apply a style to an embedded SVG?

Short answer: no, since styles don’t apply across document boundaries.

However, since you have an <object> tag you can insert the stylesheet into the svg document using script.

Something like this, and note that this code assumes that the <object> has loaded fully:

var svgDoc = yourObjectElement.contentDocument;
var styleElement = svgDoc.createElementNS("http://www.w3.org/2000/svg", "style");
styleElement.textContent = "svg { fill: #fff }"; // add whatever you need here
svgDoc.getElementById("where-to-insert").appendChild(styleElement);

It’s also possible to insert a <link> element to reference an external stylesheet:

var svgDoc = yourObjectElement.contentDocument;
var linkElm = svgDoc.createElementNS("http://www.w3.org/1999/xhtml", "link");
linkElm.setAttribute("href", "https://stackoverflow.com/questions/4906148/my-style.css");
linkElm.setAttribute("type", "text/css");
linkElm.setAttribute("rel", "stylesheet");
svgDoc.getElementById("where-to-insert").appendChild(linkElm);

Yet another option is to use the first method, to insert a style element, and then add an @import rule, e.g styleElement.textContent = "@import url(my-style.css)".

Of course you can directly link to the stylesheet from the svg file too, without doing any scripting. Either of the following should work:

<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet href="https://stackoverflow.com/questions/4906148/my-style.css" type="text/css"?>
<svg xmlns="http://www.w3.org/2000/svg">
  ... rest of document here ...
</svg>

or:

<svg xmlns="http://www.w3.org/2000/svg">
  <defs>
    <link href="https://stackoverflow.com/questions/4906148/my-style.css" type="text/css" rel="stylesheet" 
          xmlns="http://www.w3.org/1999/xhtml"/>
  </defs>
  ... rest of document here ...
</svg>

Update 2015: you can use jquery-svg plugin for apply js scripts and css styles to an embedded SVG.

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