Developer Diego Ruiz has come up with a solution called HideTab that does just that. You can very quickly hide one or all open tabs with a keyboard shortcut or right-click contextual menu. This means the tabs can't be seen both along the top of your browser, and in the list of open sites. Instead, you can only see what you've hidden in a small, and subtle pop-up menu that sits in the bottom-right-hand corner of your browser. There's also a keyboard shortcut that restores all of the tabs you've hidden.
One thing to keep in mind is that hidden tabs still continue to run in the background, which means if you're watching a video or listening to music it's going to keep playing. Hopefully a future version will provide the option to mute the audio from any tabs that are hidden.
Beyond privacy, this add-on can be a useful tool for leaning down the number of tabs you want to see. I regularly do tasks in my browser that involve hopping around to a few specific tabs, and sometimes it's nice to hone down to just those few without transferring them to a new window or doing a lot of reorganizing.
HideTab is an experimental extension, which means there may be a few bugs that have not been worked out prior to its review by the Mozilla community.