In billboard advertisement, a number of digital billboards are owned by an influence provider, and several commercial houses (which we call advertisers) approach the influence provider for a specific number of views of their advertisement content on a payment basis. Though the billboard slot allocation problem has been studied in the literature, this problem still needs to be addressed from a fairness point of view. In this paper, we introduce the Fair Billboard Slot Allocation Problem, where the objective is to allocate a given set of billboard slots among a group of advertisers based on their demands fairly and efficiently. As fairness criteria, we consider the maximin fair share, which ensures that each advertiser will receive a subset of slots that maximizes the minimum share for all the advertisers. We have proposed a solution approach that generates an allocation and provides an approximate maximum fair share. The proposed methodology has been analyzed to understand its time and space requirements and a performance guarantee. It has been implemented with real-world trajectory and billboard datasets, and the results have been reported. The results show that the proposed approach leads to a balanced allocation by satisfying the maximin fairness criteria. At the same time, it maximizes the utility of advertisers.