Incomplete multiview clustering (IMVC) focuses on exploiting the complementary and consistent information from multiple incomplete views for dividing unlabeled multiview data into corresponding clusters. Most existing methods seek to recover the missing samples of the views while inevitably having an influence on the intrinsic structure of the original space. Moreover, previous IMVC algorithms treat the samples of each view equally, which learns the consensus representation in a view-level manner and thus neglects that different views contribute to each individual sample diversely. These situations are a limitation to effective recovery of absent samples and fuse the heterogeneous information, which leads to suboptimal clustering performance. To tackle the above issues, this article proposes a novel approach called tensorized fine-grained IMVC via intrinsic structure recovery (TFIR), which flexibly recovers the intrinsic structure of the original data and attains the unified representation based on the fine-grained fusion strategy. Specifically, TFIR infers the incomplete data via available instances’ relations to improve the accuracy of learned intersample-specific representations. Afterward, TFIR stacks the specific representations of multiple views into a tensor to preserve the intrasample consistency. Finally, TFIR explores the complementarity among various views from the fine-grained sample perspective to obtain a rich underlying structure for clustering. Experimental results on the eight benchmark datasets clearly verify the remarkable superiority of TFIR compared with the most state-of-the-art methods.