It is well known that the Prandtl boundary layer equation is instable, and the well-posedness in Sobolev space for the Cauchy problem is an open problem. Recently, under the Oleinik's monotonicity assumption for the initial datum, Alexandre-Wang-Xu-Yang have proved the local well-posedness of Cauchy problem in Sobolev space. In this work, we study the Gevrey smoothing effects of the local solution obtained in [AWXY]. We prove that the Sobolev's class solution belongs to some Gevrey class with respect to tangential variables at any positive time, meaning that the Prandtl equation is hypoellitic in Gevery class.