Multi-winner social choice considers the problem of selecting a slate of K options to realize some social objective. It has found application in the construction of political legislatures and committees, product recommendation, and related problems, and has recently attracted attention from a computational perspective. We address the multi-winner problem when facing incomplete voter preferences, using the notion of minimax regret to determine a robust slate of options in the presence of preference uncertainty. We analyze the complexity of this problem and develop new exact and greedy robust optimization algorithms for its solution. Using these techniques, we also develop preference elicitation heuristics which, in practice, allow us to find near-optimal slates with considerable savings in the preference information required vis-à-vis complete votes.