Complex software systems, e.g., Cyber-Physical Systems (CPSs), interact with the real world; thus, they often behave unexpectedly in uncertain environments. Testing such systems is challenging due to limited resources, time, complex testing infrastructure setup, and the inherent uncertainties in their operating environment. Devising uncertainty-aware testing solutions supported with test optimization techniques can be considered as a mandate for tackling this challenge. This paper proposes an uncertainty-aware and time-aware test case prioritization approach, named UncerPrio, for optimizing a sequence of tests to execute with a multi-objective search. To guide the prioritization with uncertainty, we identify four uncertainty measures: uncertainty measurement (AUM), uncertainty space (PUS), the number of uncertainties (ANU), and uncertainty coverage (PUU). Based on these measures and their combinations, we proposed 10 uncertainty-aware and multi-objective test case prioritization problems, and each problem was additionally defined with one cost objective (execution cost, PET) to be minimized and one effective measure (model coverage, PTR) to be maximized. Moreover, considering time constraints for test executions (i.e., time-aware), we defined 10 time budgets for all the 10 problems for identifying the best strategy in solving uncertainty-aware test prioritization. In our empirical study, we employed four well-known Multi-Objective Search Algorithms (MuOSAs): NSGA-II, MOCell, SPEA2, and CellDE with five use cases from two industrial CPS subject systems, and used Random Algorithm (RS) as the comparison baseline. Results show that all the MuOSAs significantly outperformed RS. The strategy of Prob.6 f(PET,PTR,AUM,ANU) (i.e., the problem with uncertainty measures AUM and ANU combined) achieved the overall best performance in observing uncertainty when using 100% time budget.