<p>This paper is concerned with a class of uncertain conic multiobjective semi-infinite programming problems with vanishing constraints (abbreviated as UMSIPVCs) in the framework of Riemannian manifolds. We formulate the robust counterpart of UMSIPVC, that is, the robust conic multiobjective semi-infinite programming problem with vanishing constraints (abbreviated as RMSIPVC). By employing the powerful tools of Mordukhovich limiting subdifferential, we introduce several constraint qualifications for RMSIPVC, namely the Abadie constraint qualification (abbreviated as ACQ), the basic constraint qualification (abbreviated as BCQ), and the regular constraint qualification (abbreviated as RCQ). Moreover, the interrelationships among ACQ, BCQ, and RCQ are investigated, which further ensures that RCQ is the weakest constraint qualification. In addition, by employing the RCQ, we establish the Karush–Kuhn–Tucker (abbreviated as KKT)-type necessary optimality criteria for RMSIPVC. Several examples are provided to demonstrate the validity of the results established in this paper. To the best of our knowledge, the class of UMSIPVCs has not yet been studied in the framework of Riemannian manifolds, and the results of this paper are new even in Euclidean space.</p>