The model selection aims to adaptively match DNN model variants in edge intelligence with the limited resources of edge servers to handle Deep Learning Tasks (DLTs) efficiently. However, existing approaches often adopt a best-effort manner to maximize the system-level inference accuracy, leading to some DLTs suffering unfairness. To this end, we propose a Fair DNN Model Selection algorithm for collaborative edge intelligence (FairMS), aiming to ensure minimum inference accuracy fairly across DLTs while efficiently utilizing edge server resources. Specifically, we first formulate a joint optimization problem of inference accuracy and operational cost. Given the complexity of the problem, we then develop a DNN model selection strategy based on online learning for each edge server individually, enabling real-time and accurate solutions to the above problem. Finally, to further explore the potential of edge intelligence, we design a water-like task migration strategy for homogeneous DNN model instances and a collaborative edge computing task migration scheme for heterogeneous DNN model instances. These strategies aim to achieve finer-grained collaborative DNN selection by fostering cooperation among edge servers, thereby alleviating packet loss and efficiently utilizing idle resources. Extensive experimental tests demonstrate the advantages of the proposed FairMS in terms of the average accuracy, fairness index, and success ratio.