As you may have noticed, you can't use this property for any element you created yourself.
Here's a workaround:

string sId = "Id of the element you want to change the property of";
string sInnerHtml = "The new InnerHtml string you want to set";

string sScript = @"
var oElem = document.getElementById('" + sId + @"');
if (oElem) {
  oElem.innerHTML = '" + sValue + @"'
}"

myWebBrowser.Document.InvokeScript("execScript", new Object[] { sScript, "JavaScript" });

Sorry, forgot to write, which classes I was writing about.

myWebBrowser is an instance of System.Windows.Forms.WebBrowser

Cool.
Be sure to mark things like this as a code snippet next time.