As language models become increasingly integrated into our digital lives, Personalized Text Generation (PTG) has emerged as a pivotal component with a wide range of applications. However, the bias inherent in user written text, often used for PTG model training, can inadvertently associate different levels of linguistic quality with users' protected attributes. The model can inherit the bias and perpetuate inequality in generating text w.r.t. users' protected attributes, leading to unfair treatment when serving users. In this work, we investigate fairness of PTG in the context of personalized explanation generation for recommendations. We first discuss the biases in generated explanations and their fairness implications. To promote fairness, we introduce a general framework to achieve measure-specific counterfactual fairness in explanation generation. Extensive experiments and human evaluations demonstrate the effectiveness of our method.