Feature engineering for Electronic Health Records (EHR) is complicated by irregular observation intervals, variable measurement frequencies, and structural sparsity inherent to clinical time series. Existing automated methods either lack clinical domain awareness or assume clean, regularly sampled inputs, limiting their applicability to real-world EHR data. We present \textbf{FeatEHR-LLM}, a framework that leverages Large Language Models (LLMs) to generate clinically meaningful tabular features from irregularly sampled EHR time series. To limit patient privacy exposure, the LLM operates exclusively on dataset schemas and task descriptions rather than raw patient records. A tool-augmented generation mechanism equips the LLM with specialized routines for querying irregular temporal data, enabling it to produce executable feature-extraction code that explicitly handles uneven observation patterns and informative sparsity. FeatEHR-LLM supports both univariate and multivariate feature generation through an iterative, validation-in-the-loop pipeline. Evaluated on eight clinical prediction tasks across four ICU datasets, our framework achieves the highest mean AUROC on 7 out of 8 tasks, with improvements of up to 6 percentage points over strong baselines. Code is available at github.com/hojjatkarami/FeatEHR-LLM.