We have seen significant growth in the area of building Natural Language Processing (NLP) tools for African languages. However, the evaluation of gender bias in the machine translation systems for African languages is not yet thoroughly investigated. This is due to the unavailability of explicit text data available for addressing the issue of gender bias in machine translation. In this paper, we use transfer learning techniques based on a pre-trained Marian MT model for building machine translation models for English-Luganda and Luganda-English. Our work attempts to evaluate and quantify the gender bias within a Luganda-English machine translation system using Word Embeddings Fairness Evaluation Framework (WEFE). Luganda is one of the languages with gender-neutral pronouns in the world, therefore we use a small set of trusted gendered examples as the test set to evaluate gender bias by biasing word embeddings. This approach allows us to focus on Luganda-English translations with gender-specific pronouns, and the results of the gender bias evaluation are confirmed by human evaluation. To compare and contrast the results of the word embeddings evaluation metric, we used a modified version of the existing Translation Gender Bias Index (TGBI) based on the grammatical consideration for Luganda.