Drug repurposing or repositioning (DR) refers to finding new therapeutic applications for existing drugs. Current computational DR methods face data representation and negative data sampling challenges. Although retrospective studies attempt to operate various representations, it is a crucial step for an accurate prediction to aggregate these features and bring the associations between drugs and diseases into a unified latent space. In addition, the number of unknown associations between drugs and diseases, which is considered negative data, is much higher than the number of known associations, or positive data, leading to an imbalanced dataset. In this regard, we propose the DrugRep-KG method, which applies a knowledge graph embedding approach for representing drugs and diseases, to address these challenges. Despite the typical DR methods that consider all unknown drug-disease associations as negative data, we select a subset of unknown associations, provided the disease occurs because of an adverse reaction to a drug. DrugRep-KG has been evaluated based on different settings and achieves an AUC-ROC (area under the receiver operating characteristic curve) of 90.83% and an AUC-PR (area under the precision-recall curve) of 90.10%, which are higher than in previous works. Besides, we checked the performance of our framework in finding potential drugs for coronavirus infection and skin-related diseases: contact dermatitis and atopic eczema. DrugRep-KG predicted beclomethasone for contact dermatitis, and fluorometholone, clocortolone, fluocinonide, and beclomethasone for atopic eczema, all of which have previously been proven to be effective in other studies. Fluorometholone for contact dermatitis is a novel suggestion by DrugRep-KG that should be validated experimentally. DrugRep-KG also predicted the associations between COVID-19 and potential treatments suggested by DrugBank, in addition to new drug candidates provided with experimental evidence. The data and code underlying this article are available at https://github.com/CBRC-lab/DrugRep-KG.