The production of single-walled inorganic nanotubes is challenging due to the energetic favorability of multi-walled structures during synthesis. CrI, a layered ferromagnetic insulator, has gained significant attention as the first stand-alone monolayer ferromagnet, sparking interest in two-dimensional magnetic materials. Here, we report the synthesis of high-quality, monolayer CrI nanotubes encapsulated within multiwalled carbon nanotubes (MWCNTs), ranging from 2 to 10 nm with an average diameter of 5.3 nm, as well as a smaller amount of CrI nanorods. Through aberration-corrected transmission electron microscopy, X-ray magnetic circular dichroism (XMCD) spectroscopy, and first-principles calculations, we explored the fundamental physics and magnetism of these 1D van der Waals heterostructures. These findings pave the way towards the exploration of non-collinear magnetic states in tubular geometries, driven by the interplay of magnetic anisotropy and curvature.