Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, one of which is an outlier. Observations in the outlier sequence are generated by a unique mechanism, different from that generating the observations in all other sequences. The goal is to design a universal test to best discern the outlier sequence with the fewest observations on average. Based on the Multihypothesis Sequential Probability Ratio Test and the generalized likelihood test, a universal test is proposed and shown to be universally exponentially consistent. A lower bound on the achievable error exponents of such a test is derived. The proposed test can be modified to accommodate an additional null hypothesis with no outlier. In particular, it is shown to be consistent under the null hypothesis while retaining universally exponential consistency under all other hypotheses.