A fundamental challenge of over-parameterized deep learning models is learning meaningful data representations that yield good performance on a downstream task without over-fitting spurious input features. This work proposes MaskTune, a masking strategy that prevents over-reliance on spurious (or a limited number of) features. MaskTune forces the trained model to explore new features during a single epoch finetuning by masking previously discovered features. MaskTune, unlike earlier approaches for mitigating shortcut learning, does not require any supervision, such as annotating spurious features or labels for subgroup samples in a dataset. Our empirical results on biased MNIST, CelebA, Waterbirds, and ImagenNet-9L datasets show that MaskTune is effective on tasks that often suffer from the existence of spurious correlations. Finally, we show that \method{} outperforms or achieves similar performance to the competing methods when applied to the selective classification (classification with rejection option) task. Code for MaskTune is available at https://github.com/aliasgharkhani/Masktune.