Hyperspectral images (HSIs) are often contaminated by several types of noise, which significantly limits the accuracy of subsequent applications. Recently, low-rank modeling based on tensor singular value decomposition (T-SVD) has achieved great success in HSI restoration. Most of them use the convex and nonconvex surrogates of the tensor rank, which cannot well approximate the tensor singular values and obtain suboptimal restored results. We suggest a novel HSI restoration model by introducing a fibered rank constrained tensor restoration framework with an embedded plug-and-play (PnP)-based regularization (FRCTR-PnP). More precisely, instead of using the convex and nonconvex surrogates to approximate the fibered rank, the proposed model directly constrains the tensor fibered rank of the solution, leading to a better approximation to the original image. Since exploiting the low-fibered-rankness of HSI is mainly to capture the global structure, we further employ an implicit PnP-based regularization to preserve the image details. Particularly, the above two building blocks are complementary to each other, rather than isolated and uncorrelated. Based on the alternating direction multiplier method (ADMM), we propose an efficient algorithm to tackle the proposed model. For robustness, we develop a three-directional randomized T-SVD (3DRT-SVD), which preserves the intrinsic structure of the clean HSI and removes partial noise by projecting the HSI onto a low-dimensional essential subspace. Extensive experimental results including simulated and real data demonstrate that the proposed method achieves superior performance over compared methods in terms of quantitative evaluation and visual inspection.