We report on near-infrared supercontinuum generation in a submeter-long single-mode, nanostructured core fiber. The fiber core is composed of few thousand pure silica and germanium-doped silica glass nanorods with diameter of 200 nm each. The nanorods’ distribution is calculated based on the Maxwell–Garnett effective medium approach to mimic effective parabolic refractive index distribution in the fiber core. The standard stack-and-draw method was used to scale down the fiber structure and obtain subwavelength nanorods in the core. Size and distribution of individual nanorods are essential to determine modal and dispersion properties of the fiber without assistance of air holes in the fiber cladding. We study supercontinuum generation performance in this nanostructured core fiber pumping with low-cost microchip laser operating at 1550 nm with 1 ns pulse length and pulse energy of 0.4 µJ. A modulation instability-driven supercontinuum is generated in the fiber, covering a wavelength span of 1400–2300 nm. Due to possibility of dispersion engineering and all-solid structure the nanostructured fibers offer new possibilities for development of low-cost all-fiber supercontinuum light sources for the near-infrared range and cascaded ultrabroadband supercontinuum all-fiber systems.