$re = '/\[([^\[\]]++|(?R))*+\]/';
$str = '<p>A body of text with a media module element embedded.<p>[[{"fid":"1234","view_mode":"full","type":"media","attributes":{"height":281,"width":224,"style":"float: right;","alt":"image caption","title":"Image name","class":"media-element file-full"}}]]<p>Proin faucibus ullamcorper sapien. In viverra faucibus imperdiet. Proin a libero vulputate, imperdiet turpis eu, congue arcu. Quisque id nullam.</p>
';
preg_match($re, $str, $matches, PREG_OFFSET_CAPTURE, 0);
// Print the entire match result
var_dump($matches);
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php