I have the following packages and their dependencies installed in my WebAPI project:
Ninject.Web.WebApi Ninject.Web.WebApi.OwinHost
Ninject.Web.WebApi
Ninject.Web.WebApi.OwinHost
What worked for me was adding the NuGet package Ninject.Web.WebApi.WebHost as described here: https://github.com/ninject/Ninject.Web.WebApi/wiki/Setting-up-an-mvc-webapi-application
Ninject.Web.WebApi.WebHost