In this work, we present for the first time a laser-based dual gas sensor utilizing a silica-based Antiresonant Hollow-Core Fiber (ARHCF) operating in the Near- and Mid-Infrared spectral region. A 1-m-long fiber with an 84-µm diameter air-core was implemented as a low-volume absorption cell in a sensor configuration utilizing the simple and well-known Wavelength Modulation Spectroscopy (WMS) method. The fiber was filled with a mixture of methane (CH4) and carbon dioxide (CO2), and a simultaneous detection of both gases was demonstrated targeting their transitions at 3.334 µm and 1.574 µm, respectively. Due to excellent guidance properties of the fiber and low background noise, the proposed sensor reached a detection limit down to 24 parts-per-billion by volume for CH4 and 144 parts-per-million by volume for CO2. The obtained results confirm the suitability of ARHCF for efficient use in gas sensing applications for over a broad spectral range. Thanks to the demonstrated low loss, such fibers with lengths of over one meter can be used for increasing the laser-gas molecules interaction path, substituting bulk optics-based multipass cells, while delivering required flexibility, compactness, reliability and enhancement in the sensor’s sensitivity.