Foundation models pre-trained on large-scale source datasets are reshaping the traditional training paradigm for time series classification. However, existing time series foundation models primarily focus on forecasting tasks and often overlook classification-specific challenges, such as modeling interpretable shapelets that capture class-discriminative temporal features. To bridge this gap, we propose UniShape, a unified shape-aware foundation model designed for time series classification. UniShape incorporates a shape-aware adapter that adaptively aggregates multiscale discriminative subsequences (shapes) into class tokens, effectively selecting the most relevant subsequence scales to enhance model interpretability. Meanwhile, a prototype-based pretraining module is introduced to jointly learn instance- and shape-level representations, enabling the capture of transferable and class-discriminative shape patterns. Pre-trained on a large-scale multi-domain time series dataset comprising 1.89 million samples, UniShape exhibits superior generalization across diverse target domains. Experiments on 128 UCR datasets and 30 additional time series datasets demonstrate that UniShape achieves state-of-the-art classification performance, with interpretability and ablation analyses further validating its effectiveness.