I was just trying to install the new version of Google APIs Client Library, and ran across this error message. This was a new error message to me.
This error message is telling me that there is a new version of NuGet and if I want to install the package, then I have to use the new version of NuGet. If you go to the Tools -> Extension manager menu in visual studio you will find a list of installed extensions. Once you have found NuGet you will be allowed to update it.
Once it is updated you will then have to restart Visual studio and you will be able to install your package.
Some packages can only be installed with the newest version of NuGet package manager. If you see the “package requires NuGet client version” you know that you need to upgrade to a new version of NuGet, before you will be able to install the package.