I do not store ribbon in my Stash and Store - 5 Drawer Supply Cases. I don’t know the size of your ribbon but I do have a few narrow rolls of washi tape that measure 1⅝” in diameter. Eighteen of them will fit in one of the divided sections. The drawer will easily hold six 2” rolls of washi tape in each divided section.
I purchased my Stash and Store - 5 Drawer Supply Cases for my large and growing embossing powder and glitter collection. I removed the dividers. Each drawer is pretty full and I’ve had no problems with the sturdiness of the drawers or the unit.