Most current few-shot learning methods train a model from abundantly labeled base category data and then transfer and adapt the model to sparsely labeled novel category data. These methods mostly generalize well on novel categories from the same domain as the base categories but perform poorly for distant domain categories. In this paper, we propose a framework for few-shot learning coined as ConFeSS (Contrastive Learning and Feature Selection System) that tackles large domain shift between base and novel categories. The first step of our framework trains a feature extracting backbone with the contrastive loss on the base category data. Since the contrastive loss does not use supervision, the features can generalize better to distant target domains. For the second step, we train a masking module to select relevant features that are more suited to target domain classification. Finally, a classifier is fine-tuned along with the backbone such that the backbone produces features similar to the relevant ones. To evaluate our framework, we tested it on a recently introduced cross-domain few-shot learning benchmark. Experimental results demonstrate that our framework outperforms all meta-learning approaches and produces competitive results against recent cross-domain methods. Additional analyses are also performed to better understand our framework.