The model of random interlacements on ℤd, d≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter u parametrizes the density of random interlacements on ℤd. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level u, in the non-percolative regime u>u∗, with u∗ the non-degenerate critical parameter for the percolation of the vacant set, see [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints], [Comm. Pure Appl. Math. 62 (2009) 831–858]. We prove a stretched exponential decay of the connectivity function for the vacant set at level u, when u>u∗∗, where u∗∗ is another critical parameter introduced in [Ann. Probab. 37 (2009) 1715–1746]. It is presently an open problem whether u∗∗ actually coincides with u∗.