Regression testing is used to validate modified source code. Multitenant SaaS applications need to continuously evolve due to the various configuration needs of multiple tenants. Due to time and resource constraints, traditional regression testing is inefficient, that re-executes the entire test suite when an application undergoes change. This study introduces a novel multi-criteria test case prioritization approach for multitenant SaaS applications. Test case prioritization orders the test cases to achieve a certain goal, such as optimizing the fault detection. Traditional prioritization methods often rely on single factors, limiting their effectiveness in complex multitenant SaaS applications. The proposed multi-criteria prioritization technique integrates dependency-based and risk-based prioritization techniques to effectively prioritize the test cases. Dependency-based prioritization focuses on prioritizing the test cases by identifying the modules dependent on modified modules of an application. Risk-based prioritization prioritizes the test cases by assigning the risk levels. A prioritization matrix is built, with each test case receiving a priority score based on its dependency-priority level and risk-priority level. This priority score defines the sequence of the execution of test cases where all test cases are executed in descending order of their priority score. The effectiveness of the approach is measured using a metrics Average Percentage of Faults Detected (APFD) metric. The proposed approach is empirically evaluated with a multitenant SaaS MtBookTrip application in terms of its fault detection rate. The results demonstrate that proposed multi-criteria approach achieved an APFD value of 0.9, while the random order technique resulted in an APFD of 0.61. The prioritized test suite has a higher APFD value than the random technique, indicating faster fault discovery during regression testing.