Analysis of the fairness of machine learning (ML) algorithms recently attracted many researchers' interest. Most ML methods show bias toward protected groups, which limits the applicability of ML models in many applications like crime rate prediction etc. Since the data may have missing values which, if not appropriately handled, are known to further harmfully affect fairness. Many imputation methods are proposed to deal with missing data. However, the effect of missing data imputation on fairness is not studied well. In this paper, we analyze the effect on fairness in the context of graph data (node attributes) imputation using different embedding and neural network methods. Extensive experiments on six datasets demonstrate severe fairness issues in missing data imputation under graph node classification. We also find that the choice of the imputation method affects both fairness and accuracy. Our results provide valuable insights into graph data fairness and how to handle missingness in graphs efficiently. This work also provides directions regarding theoretical studies on fairness in graph data.