Named string interpolation
Always check the argument which is reffered by this in an extension method against null to early throw and return. Sure one could say it doesn't matter, because it will throw an ArgumentNullException but that would be thrown from the Regex.Split() method.  
You don't check for args == null either. 
The optional argument ignoreCase isn't used anywhere in that method so it can safely removed.  
if by accident the property of the anonymous object isn't spelled exactly like in the string, the call to argsType.GetProperty() will return null and an NullReferenceException is thrown. Maybe it would be better for such a case to just assume it isn't a property. I will come back to this later.  
if the passed in text only contains { the code will throw an IndexOutOfRange exception. This can be prevented by returning early if the length of text is &lt; 3.  
if the Length of substrings will be &lt; 3 we can return early by returning text.  
the regex pattern does not allow single letter variables being passed. So a text like {i} won't be matched.  


Implementing the mentioned points will lead to  

public static string FormatFrom(this string text, object args)
{
    if (text == null) { throw new ArgumentNullException("text"); }

    if (text.Length &lt; 3 || string.IsNullOrWhiteSpace(text) || args==null) { return text; }

    var substrings = Regex.Split(text, "({{?)([A-Za-z_][A-Za-z0-9_]+)(}}?)")
                          .Where(s =&gt; s != string.Empty).ToArray();

    if (substrings.Length &lt; 3) { return text; }

    var argsType = args.GetType();
    var result = new StringBuilder(text.Length);

    const int propertyNameOffset = 1;
    const int rightBraceOffset = 2;

    var bindingFlags = BindingFlags.Instance | BindingFlags.Public;

    for (int i = 0; i &lt; substrings.Length; i++)
    {

        var possibleLeftBraces = substrings[i];
        var possibleRightBraces = substrings[i + rightBraceOffset];
        var propertyName = substrings[i + propertyNameOffset];

        var isPropertyName = possibleLeftBraces == "{" &amp;&amp; possibleRightBraces == "}";
        if (isPropertyName)
        {
            var property = argsType.GetProperty(propertyName, bindingFlags);
            if (property == null)
            {
                result.Append("{").Append(propertyName).Append("}");
            }
            else
            {
                result.Append(property.GetValue(args, null));
            }
            i += 2;
            continue;
        }

        var isEscapedPropertyName = possibleLeftBraces == "{{" &amp;&amp; possibleRightBraces == "}}";
        if (isEscapedPropertyName)
        {
            result.Append("{").Append(propertyName).Append("}");
            i += 2;
            continue;
        }

        result.Append(substrings[i]);
    }

    return result.ToString();
}  


which will pass all of these tests  

[TestMethod()]
public void FormatFromTestStringEmptyShouldPass()
{
    string expected = string.Empty;
    string actual = string.Empty.FormatFrom(null);

    Assert.AreEqual(expected, actual);

}
[TestMethod(),ExpectedException(typeof(ArgumentNullException))]
public void FormatFromTestStrinNullShouldPass()
{

    string actual = ((string)null).FormatFrom(null);

    Assert.Inconclusive("Shouldn't happen !");

}
[TestMethod()]
public void FormatFromTestArgsNullShouldPass()
{
    string expected = "lala";
    string actual = "lala".FormatFrom(null);

    Assert.AreEqual(expected, actual);

}
[TestMethod()]
public void FormatFromTestParamsButArgsNullShouldPass()
{
    string expected = "{land}";
    string actual = "{land}".FormatFrom(null);

    Assert.AreEqual(expected, actual);

}
[TestMethod()]
public void FormatFromTestArgsNotNullShouldPass()
{
    string expected = "germany";
    string actual = "{land}".FormatFrom(new { land = "germany" });
    Assert.AreEqual(expected, actual);

}
[TestMethod()]
public void FormatFromTestArgsNotNullButWrongShouldPass()
{
    string expected = "{land}"; // TODO: Passenden Wert initialisieren
    string actual;
    actual = "{land}".FormatFrom(new { lan = "germany" });
    Assert.AreEqual(expected, actual);
}