Machine translation is an active area of research that has received a significant amount of attention over the past decade. With the advent of deep learning models, the translation of several languages has been performed with high accuracy and precision. In spite of the development in machine translation techniques, there is very limited work focused on translating low-resource African languages, particularly Nigerian languages. Nigeria is one of the most populous countries in Africa with diverse language and ethnic groups. In this paper, we survey the current state of the art of machine translation research on Nigerian languages with a major emphasis on neural machine translation techniques. We outline the limitations of research in machine translation on Nigerian languages and propose future directions in increasing research and participation.