We propose a monolithic narrowband guided-mode grating filter in fused silica that is widely tunable in the near-IR wavelength region. Based on a recently demonstrated approach for a monolithic reflector comprising an encapsulated grating, we theoretically investigate such a device by means of rigorous modeling aimed at a narrow linewidth. It is demonstrated that upon a spatial variation of the filter's grating period its resonance wavelength can be tuned in a remarkably wide range of near-IR radiation with 800 nm<λ(res)< 1600 nm by translating the laser beam relative to the grating area. The filter performance in terms of linewidth and contrast is essentially preserved over the entire tuning interval.