In addition to Peter's answer, if you want to stay with property and property injection, you can add "immutability" manually by code, something like that:
public class Config
{
private string _connectionString;
public String ConnectionString
{
get
{
return _connectionString;
}
set
{
if (_connectionString != null) throw new ReadOnlyException("_connectionString");
if (value == null) throw new ArgumentNullException("value");
_connectionString = value;
}
}
}