Today, within intense global competition in the financial sector, the financial institutions are striving to sustain themselves, leading to a growing emphasis on environmental, social, and governance practices towards sustainability in finance. In addition, within the huge technological development, the potential of Blockhain technology technology to improve financial sustainability is attracting increasing attention and financial institutions are focusing on Blockchain technology adoption for sustainable finance which is a topic that is not yet well-studied. Studies attempting to find novel answers that strike a balance between promoting economic growth, protecting the environment, and ensuring social well-being are getting high interest. The paper synthesizes through a PRISMA systematic literature, financial institutions, Blockchain technology adoption, sustainable finance, and Environmental, Social and Governance practices. It highlights the regulatory challenges and technical barriers to blockchain adoption, as well as the potential of blockchain to enable more sustainable finance practices. Moreover, it presents suggestions for moving the literature forward and discusses implications addressed to financial institutions.