In this paper, we give some sharp estimates for the first non-zero eigenvalue of Paneitz operators of an $n$-dimensional embedded closed hypersurface in a Euclidean space in terms of the mean curvature and the $Q$-curvature. Furthermore, we also give some isoperimetric upper bounds for the first non-zero eigenvalue of the $p$-Laplace operator of an $n$-dimensional embedded closed hypersurface in a Euclidean space.