We investigate the Fourier dimension, \(\dim _F\mu \) , of Mandelbrot multiplicative cascade measures \(\mu \) on the d-dimensional unit cube. We show that if \(\mu \) is the cascade measure generated by a sub-exponential random variable, then \(\begin{aligned} \dim _F\mu =\min \{2,\dim _2\mu \}, \end{aligned}\) where \(\dim _2\mu \) is the correlation dimension of \(\mu \) and it has an explicit formula. For cascades on the circle \(S\subset \mathbb {R}^2\) , we obtain \(\begin{aligned} \dim _F\mu \ge \frac{\dim _2\mu }{2+\dim _2\mu }. \end{aligned}\)
