Interaction of terahertz (THz) radiation with van der Waals semiconductors represents a considerable interest for optoelectronic applications. Here we report a redshift (around 1 meV) of the trion resonance in the MoSe₂ monolayer induced by picosecond THz pulses. As its origin, we identify the kinetic excess energy gained by hot carriers due to absorption of THz light which is transferred during the formation of trions. By performing time-resolved measurements, we have determined the electron cooling time (τ = 70 ps) and estimated the absorption at 7.7 THz (α = 0.3%). A quantitative model based on the Heisenberg equation of motion explains the experimental observations and can reproduce the data with good accuracy. The present work gives important insights for understanding the trions in van der Waals semiconductors and their interaction with hot electrons driven by THz radiation.