Thankfully for those going digital, Nintendo of Japan has updated the game's store page with more details regarding its file size. I'm sure that Super Mario Odyssey will be a big game where it will offer lots of content. This isn't including any sort of potential day one patches. For comparison, Super Mario 3D World took 1.7GB on Wii U, Mario + Rabbids Kingdom Battle requires 2.3GB, while the Switch's other heavy hitter, the Legend of Zelda: Breath of the Wild, is 13.4GB pre-DLC.
With Nintendo being the main developer of the game, it's no surprise at all that their games are compressed pretty well.
For those looking to boost their console's storage, Nintendo has stated that increasing the size can be done with MicroSD, MicroSDHC, or MicroSDXC memory cards.
The Direct presentation by Nintendo gave us an insight of what to expect from the Super Mario Odyssey game and one of the things that were highlighted in the presentation was the new outfits that Mario will be getting for his adventures.