The large transparency window of silicon, covering the 1.1 um 8 um wavelength range, makes it a promising platform for the implementation of photothermal-based absorption spectrometers. These devices indirectly sense absorption in the mid-infrared (MIR) by using near-infrared (NIR) wavelengths, thereby enabling the realization of MIR absorption spectrometers without the need for MIR photodetectors. Nevertheless, due to their comparatively large index contrast and cross-sections, MIR Si strip waveguides are multi-mode at NIR wavelengths, hindering device implementation. Here we present, for the first time, an integrated Bragg grating waveguide filter for hybrid near- and mid-infrared operation. Specifically, the filter is implemented in a single-etch suspended silicon corrugated waveguide with an effectively single-mode operation in NIR region for a waveguide cross-section as large as 0.5 um x 1.1 um. At the same time, the waveguide supports single-mode propagation in MIR region. We demonstrate a long-period waveguide Bragg grating yielding a sharp third-order Bragg resonance for the fundamental waveguide mode and radiating the higher order modes. We experimentally demonstrate a notch filter with a 4nm bandwidth and 40 dB extinction ratio with a temperature-dependent Bragg wavelength shift of 70pm/K.