The low-frequency amplitude and phase noise spectra of magnetization waves, i.e. magnons, was measured in the yttrium iron garnet (YIG) waveguides. This type of noise, which originates from the fluctuations of the physical properties of the YIG crystals, has to be taken into account in the design of YIG-based RF generators and magnonic devices for data processing, sensing and imaging applications. It was found that the amplitude noise level of magnons depends strongly on the power level, increasing sharply at the on-set of nonlinear dissipation. The noise spectra of both the amplitude and phase noise have the Lorentzian shape with the characteristic frequencies below 100 Hz.