Bioprinting holds great promise toward engineering functional cardiac tissue constructs for regenerative medicine and as drug test models. However, it is highly limited by the choice of inks that require maintaining a balance between the structure and functional properties associated with the cardiac tissue. In this regard, a novel and mechanically robust biomaterial‐ink based on nonmulberry silk fibroin protein is developed. The silk‐based ink demonstrates suitable mechanical properties required in terms of elasticity and stiffness (≈40 kPa) for developing clinically relevant cardiac tissue constructs. The ink allows the fabrication of stable anisotropic scaffolds using a dual crosslinking method, which are able to support formation of aligned sarcomeres, high expression of gap junction proteins as connexin‐43, and maintain synchronously beating of cardiomyocytes. The printed constructs are found to be nonimmunogenic in vitro and in vivo. Furthermore, delving into an innovative method for fabricating a vascularized myocardial tissue‐on‐a‐chip, the silk‐based ink is used as supporting hydrogel for encapsulating human induced pluripotent stem cell derived cardiac spheroids (hiPSC‐CSs) and creating perfusable vascularized channels via an embedded bioprinting technique. The ability is confirmed of silk‐based supporting hydrogel toward maturation and viability of hiPSC‐CSs and endothelial cells, and for applications in evaluating drug toxicity.