Heterogeneous Information Networks (HINs) are prevalent in real-world systems. Recent advances in network embedding provide an effective way of encoding HINs into low-dimensional vectors. However, there is a growing concern that existing HIN embedding algorithms may suffer from the problem of generating biased representations, resulting in discrimination against certain demographic groups. In this paper, we propose a flexible debiasing framework for fair HIN embedding to address this issue. Specifically, we first formalize measurements and the definition of fairness in HIN embedding. Then, we propose a debiasing framework named FairHGNN, including a novel meta-path sampling method that focuses on mitigating the bias in random walks, and a fairness constraint with Wasserstein distance to alleviate the algorithmic bias in Graph Neural Networks (GNNs). Experimental results on real-world datasets validate the efficacy of FairHGNN in promoting fairness and maintaining good utility.