An interval-valued intuitionistic fuzzy sets (IVIFSs) theory, which is an effective tool for dealing with uncertainty, has attracted the attention of researchers and has been applied to many fields. One of the significant topics in intuitionistic fuzzy sets is the measure of distance. Many distance measures have been developed for IVIFSs in the literature over the last fifteen years. However, not all of these measures can satisfy the axioms of distance. In this study, a Jaccard distance measure and its proofs are extended under the IVIF environment. The proposed Jaccard distance measure is compared with the existing distance measures. The result of the analysis indicates that the proposed Jaccard distance measure overcomes the disadvantages of the current distance measures. Moreover, the extension of the TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method based on the proposed Jaccard distance is presented to solve MCDM (Multi Criteria Decision Making) problems in the IVIF environment. Finally, a personnel selection problem is solved to illustrate the proposed MCDM method.