Absorbing near-infrared (NIR) photons, with longer wavelengths, in atomically thin monolayer MoS₂ presents a significant challenge due to its weak optical absorption and narrow absorption bands. Consequently, MoS₂-based photodetector devices often experience low responsivity and a limited detection window. Herein, a novel InAs@ZnSe core@shell/1L-MoS₂ heterostructure, leveraging InAs@ZnSe as the primary infrared-absorbing material and exploiting the formation of a type-II heterostructure is showcased. Steady-state and time-resolved spectroscopy, along with optoelectronic characterization, are employed to investigate photo-induced charge transfer dynamics. The results show efficient hole transfer to InAs@ZnSe upon excitation of both materials. Instead, with selective excitation of InAs@ZnSe, electron transfer is observed from InAs@ZnSe to the 1L-MoS₂. The heterostructure demonstrates a broadband photoresponse spanning the wavelength range of 300 to 850 nm, exhibiting a Responsivity of ≈10³ A/W and Detectivity of ≈10¹¹ Jones. The signal-to-noise ratio substantially increases by 3 to 4 orders of magnitude for 700 and 850 nm excitation compared to pristine 1L-MoS₂. The enhancement in photoresponse and signal-to-noise ratio is attributed to increased absorption, which helps eliminate defect and trap states, thereby promoting the photogating effect.