Recently, black phosphorus (BP) has joined the two-dimensional material family as a promising candidate for photonic applications due to its moderate bandgap, high carrier mobility, and compatibility with a diverse range of substrates. Photodetectors are probably the most explored BP photonic devices, however, their unique potential compared with other layered materials in the mid-infrared wavelength range has not been revealed. Here, we demonstrate BP mid-infrared detectors at 3.39 μm with high internal gain, resulting in an external responsivity of 82 A/W. Noise measurements show that such BP photodetectors are capable of sensing mid-infrared light in the picowatt range. Moreover, the high photoresponse remains effective at kilohertz modulation frequencies, because of the fast carrier dynamics arising from BP's moderate bandgap. The high photoresponse at mid-infrared wavelengths and the large dynamic bandwidth, together with its unique polarization dependent response induced by low crystalline symmetry, can be coalesced to promise photonic applications such as chip-scale mid-infrared sensing and imaging at low light levels.