Organic-inorganic perovskites have attracted great interest for developing wavelength-selective photodetectors. Currently, the spectral response range of narrowband photodetectors is mainly concentrated within the visible light region, lacking near-infrared photodetectors. Here, we present perovskite narrowband near-infrared photodetectors achieved by transverse propagation of light in perovskite waveguide devices for the first time. The response spectra of photodetectors are continuously tuned from 750 to 1000 nm by changing the perovskite component and the position of the incident light with the full width at half-maximum of 25-80 nm. The theoretical and experimental results reveal that the typical perovskite photodetectors serve as an optical waveguide to confine and propagate the light, in which the long wavelength light propagates a longer distance; oppositely, the short wavelength light with the higher loss in devices fails to produce a photoresponse, owing to the wavelength dependent absorption of perovskite. This provides a new concept for designing narrowband photodetectors and will simulate new applications.