I have an image logo.png stored in both Resources and Images folder in my VB.NET project. However, this image is somehow not visible for the add-in. I've checked the add-in package (.esriAddIn zip file) after compiling the project and there is no image "logo.png" in the Images folder inside this package.

The question is: how can I include this image to my add in package?

You need to inform the build process to include the image file in the Add-In package.
In Visual Studio's solution explorer, select your logo.png file under images. Set the Build Action property to AddInContent.