Noise level is required as an input parameter in various image processing applications. In this work, we use the dark channel prior (DCP) to estimate the noise level of an image degraded by additive white Gaussian noise. We develop an approximate model of the probability density function of the dark channel of the noisy image. Using this model, the noise level is determined with the maximum likelihood estimation method from the dark channel intensity values of the noisy image. The results show that our method is faster than the state-of-the-art methods by about two orders of magnitude while providing slightly inferior estimation performance.