Magnetoacoustic investigations of the ZnSe:Cr2+ crystal with sphalerite structure, performed in Faraday geometry, show that there is a new channel of relaxation by the Cr2+ Jahn–Teller (JT) centers, induced by the magnetic field. A new method is worked out that allows to extract the relaxation time, either from the temperature changes of the elastic modulus in fixed magnetic field or from the magnetic field dependences at fixed temperatures. Application of both approaches to the imaginary part of the elastic modulus prove their efficiency and indicate that the magnetic field‐dependent relaxation rate reaches the magnitude of about 106 s−1 at T = 1.3 K.