A weighted multivariate signed-rank test is introduced for an analysis of multivariate clustered data. Observations in different clusters may then get different weights. The test provides a robust and efficient alternative to normal theory based methods. Asymptotic theory is developed to find the approximate p-value as well as to calculate the limiting Pitman efficiency of the test. A conditionally distribution-free version of the test is also discussed. The finite-sample behavior of different versions of the test statistic is explored by simulations and the new test is compared to the weighted versions of Hotelling’s T² test and the multivariate spatial sign test introduced in Larocque et al. (2007). Finally, a real data example is used to illustrate the theory.