I have the following packages and their dependencies installed in my WebAPI project:
Ninject.Web.WebApi
Ninject.Web.WebApi.OwinHost
As other answers have pointed out, the error message can be misleading. Ninject might be working fine, but it could be that some dependency cannot be instantiated for a variety of reasons, such as:
[Inject] property).You do not see all details in the error returned by the server (which may be by design). If you attach the debugger, you may also not be able to catch the exception unless you disable "Just My Code" in the debugging settings. Then you may be able to catch an internal Ninject exception which may have all the information you need to understand the problem.
Older versions of Ninject, or if you are not using Ninject.Web.WebApi.WebHost, also require that you register Ninject as a dependency resolver, as pointed out in https://stackoverflow.com/a/24196092/2279059.