Cardiovascular diseases (CVD) constitute a major fraction of the current major global diseases and lead to about 30% of the deaths, i.e., 17.9 million deaths per year. CVD include coronary artery disease (CAD), myocardial infarction (MI), arrhythmias, heart failure, heart valve diseases, congenital heart disease, and cardiomyopathy. Cardiac Tissue Engineering (CTE) aims to address these conditions, the overall goal being the efficient regeneration of diseased cardiac tissue using an ideal combination of biomaterials and cells. Various cells have thus far been utilized in pre-clinical studies for CTE. These include adult stem cell populations (mesenchymal stem cells) and pluripotent stem cells (including autologous human induced pluripotent stem cells or allogenic human embryonic stem cells) with the latter undergoing differentiation to form functional cardiac cells. The ideal biomaterial for cardiac tissue engineering needs to have suitable material properties with the ability to support efficient attachment, growth, and differentiation of the cardiac cells, leading to the formation of functional cardiac tissue. In this review, we have focused on the use of biomaterials of natural origin for CTE. Natural biomaterials are generally known to be highly biocompatible and in addition are sustainable in nature. We have focused on those that have been widely explored in CTE and describe the original work and the current state of art. These include fibrinogen (in the context of Engineered Heart Tissue, EHT), collagen, alginate, silk, and Polyhydroxyalkanoates (PHAs). Amongst these, fibrinogen, collagen, alginate, and silk are isolated from natural sources whereas PHAs are produced via bacterial fermentation. Overall, these biomaterials have proven to be highly promising, displaying robust biocompatibility and, when combined with cells, an ability to enhance post-MI cardiac function in pre-clinical models. As such, CTE has great potential for future clinical solutions and hence can lead to a considerable reduction in mortality rates due to CVD.