Tabular data sets with varying missing values are prepared for machine learning using an arbitrary imputation strategy. Synthetic values generated by imputation models often raise concerns regarding data quality and the reliability of data-driven outcomes. To address these concerns, this article proposes an imputation-free incremental attention learning (IFIAL) method for tabular data with missing values. A pair of attention masks is derived and retrofitted to a transformer to directly streamline tabular data without imputing or initializing missing values. The proposed method incrementally learns partitions of overlapping and fixed-size feature sets to enhance the performance of the transformer. The average classification performance rank order across 17 diverse tabular data sets highlights the superiority of IFIAL over 11 state-of-the-art learning methods with or without missing value imputations. Additional experiments corroborate the robustness of IFIAL to varying types and proportions of missing data, demonstrating its superiority over methods that rely on explicit imputations. A feature partition size equal to one-half the original feature space yields the best trade-off between computational efficiency and predictive performance. IFIAL is one of the first solutions that enables deep attention models to learn directly from tabular data, eliminating the need to impute missing values. %without the need for imputing missing values. The source code for this paper is publicly available.