Person re-identification in the wild needs to simultaneously (frame-wise) detect and re-identify persons and has wide utility in practical scenarios. However, such tasks come with an additional open-set re-ID challenge as all probe persons may not necessarily be present in the (frame-wise) dynamic gallery. Traditional or close-set re-ID systems are not equipped to handle such cases and raise several false alarms as a result. To cope with such challenges open-set metric learning (OSML), based on the concept of Large margin nearest neighbor (LMNN) approach, is proposed. We term our method Open-Set LMNN (OS-LMNN). The goal of separating impostor samples from the genuine samples is achieved through a joint optimization of the Weibull distribution and the Mahalanobis metric learned through this OS-LMNN approach. The rejection is performed based on low probability over distance of imposter pairs. Exhaustive experiments with other metric learning techniques over the publicly available PRW dataset clearly demonstrate the robustness of our approach.