Two-dimensional transition metal dichalcogenides (2D-TMDs) are among the most promising materials for exploring and exploiting exciton transitions. Excitons in 2D-TMDs present remarkably long lifetimes, even at room temperature. The spectral response of exciton transitions in 2D-TMDs has been thoroughly characterized over the past decade by means of photoluminescence spectroscopy, transmittance spectroscopy, and related techniques; however, the spectral dependence of their electronic response is still not fully characterized. In this work, we investigate the electronic response of exciton transitions in monolayer MoSe2 via low-temperature photocurrent spectroscopy. We identify the spectral features associated with the main exciton and trion transitions, with spectral bandwidths down to 15 meV. We also investigate the effect of the Fermi level on the position and intensity of excitonic spectral features, observing a very strong modulation of the photocurrent, which even undergoes a change in sign when the Fermi level crosses the charge neutrality point. Our results demonstrate the unexploited potential of low-temperature photocurrent spectroscopy for studying excitons in low-dimensional materials, and provide new insight into excitonic transitions in 1L-MoSe2.