Unsupervised feature selection (UFS) has received great interest in various areas of research that require dimensionality reduction, including machine learning, data mining, and statistical analysis. However, UFS algorithms are known to perform poorly on datasets with missing data, exhibiting a significant computational load and learning bias. In this work, we propose a novel and robust UFS method, designated PFA-Nipals, that works with missing data without the need for deletion or imputation. This is achieved by considering an iterative nonlinear estimation of principal components by partial least squares, while the relevant features are selected through minibatch K-means clustering. The proposed method is successfully applied to select the relevant features of a robust health dataset with missing data, outperforming other UFS methods in terms of computational load and learning bias. Furthermore, the proposed method is capable of finding a consistent set of relevant features without biasing the explained variability, even under increasing missing data. Finally, it is expected that the proposed method could be used in several areas, such as machine learning and big data with applications in different areas of the medical and engineering sciences.