Sequential recommendation aims to predict the next item a user is likely to prefer based on their sequential interaction history. Recently, text-based sequential recommendation has emerged as a promising paradigm that uses pre-trained language models to exploit textual item features to enhance performance and facilitate knowledge transfer to unseen datasets. However, existing text-based recommender models still struggle with two key challenges: (i) representing users and items with multiple attributes, and (ii) matching items with complex user interests. To address these challenges, we propose a novel model, Matching Attribute-aware Representations for Text-based Sequential Recommendation (MARS). MARS extracts detailed user and item representations through attribute-aware text encoding, capturing diverse user intents with multiple attribute-aware representations. It then computes user-item scores via attribute-wise interaction matching, effectively capturing attribute-level user preferences. Our extensive experiments demonstrate that MARS significantly outperforms existing sequential models, achieving improvements of up to 24.43% and 29.26% in Recall@10 and NDCG@10 across five benchmark datasets. Code is available at https://github.com/junieberry/MARS