This is not necessarily so.  As long as your static logger exposes a method for:
- Injection of the classes you WANT injected, or
- Injection of the DI Container in an appropriate method call prior to running it (say in something like the asp.net global.asax Application_Start method), then you should be fine.
Here's an example.  Take the following class for DI:
 public class Logger : ILogger
    {
        public void Log(string stringToLog)
        {
           Console.WriteLine(stringToLog);
        }
    }
    public interface ILogger
    {
        void Log(string stringToLog);
    }
And here's our static class which needs a logger:
public static class SomeStaticClass
    {
        private static IKernel _diContainer;
        private static ILogger _logger;
        public static void Init(IKernel dIcontainer)
        {
            _diContainer = dIcontainer;
            _logger = _diContainer.Get<ILogger>();
        }
        public static void Log(string stringToLog)
        {
            _logger.Log(stringToLog);
        }
    }
Now, in a global startup for your app (in this case, in my global.asax.cs), you can instantiate your DI Container, then hand that off to your static class.
public class Global : Ninject.Web.NinjectHttpApplication
    {
        protected override IKernel CreateKernel()
        {
            return Container;
        }
        static IKernel Container
        {
            get
            {
                var standardKernel = new StandardKernel();
                standardKernel.Bind<ILogger>().To<Logger>();
                return standardKernel;
            }
        }
        void Application_Start(object sender, EventArgs e)
        {
            SomeStaticClass.Init(Container);
            SomeStaticClass.Log("Dependency Injection with Statics is totally possible");
        }
And presto!  You are now up and running with DI in your static classes.
Hope that helps someone.  I am re-working an application which uses a LOT of static classes, and we've been using this successfully for a while now.