Cardiovascular disease is one of major causes of deaths, and its incidence has gradually increased worldwide. For cardiovascular diseases, several therapeutic approaches, such as drugs, cell-based therapy, and heart transplantation, are currently employed; however, their therapeutic efficacy and/or practical availability are still limited. Recently, biomaterial-based tissue engineering approaches have been recognized as promising for regenerating cardiac function in patients with cardiovascular diseases, including myocardial infarction (MI). In particular, materials mimicking the characteristics of native cardiac tissues can potentially prevent pathological progression and promote cardiac repair of the heart tissues post-MI. The mechanical (softness) and electrical (conductivity) properties of biomaterials as non-biochemical cues can improve the cardiac functions of infarcted hearts by mitigating myocardial cell death and subsequent fibrosis, which often leads to cardiac tissue stiffening and high electrical resistance. Consequently, electrically conductive hydrogels that can provide mechanical strength and augment the electrical activity of the infarcted heart tissue are considered new functional materials capable of mitigating the pathological progression to heart failure and stimulating cardiac regeneration. In this review, we highlight nanomaterial-incorporated hydrogels that can induce cardiac repair after MI. Nanomaterials, including carbon-based nanomaterials and recently discovered two-dimensional nanomaterials, offer great opportunities for developing functional conductive hydrogels owing to their excellent electrical conductivity, large surface area, and ease of modification. We describe recent results using nanomaterial-incorporated conductive hydrogels as cardiac patches and injectable hydrogels for cardiac repair. While further evaluations are required to confirm the therapeutic efficacy and toxicity of these materials, they could potentially be used for the regeneration of other electrically active tissues, such as nerves and muscles.