The emergence and development of systems of systems (SoSs) have expanded the complexity and adaptability of systems engineering. Due to the heterogeneity of its constituent systems, designing and analyzing an SoS faces enormous challenges. Therefore, the verification of an SoS is important in its design phase. However, related methods and techniques are still in the preliminary research state, mainly for requirements verification and system verification, and a lack of efforts in design verification for SoSs. Aiming to provide the ability to detect hazardous states at the design phase, we worked on a novel method for automatically generating test cases for model verification in SoSs. Considering the characteristics of SoSs, the method adopts fault injection and model-based system engineering as the foundations to extend the automated generation capability of test cases. This paper proposes an automatic test generation (ATG) method for an SoS based on fault injection and model-based systems engineering (MBSE). It is meant to generate test cases that can be used to check the effectiveness of fault detection or identification in SoSs and for the effective testing of their constituent systems (CSs). This paper discusses scenario generation and ATG in linear temporal logic and designs an algorithm to generate traces as test suites, taking into account the constraints of the models. By establishing a concept alignment example (CAE) as the experimental use case, three test scenarios are generated automatically, showing that the use of the proposed ATG method provides a reasonable hazardous detection capability for verification in SoS design. The main contributions of the paper are (1) the description of the proposed two-phase ATG approach with fault-centric modeling activities and generation-related activities; (2) the explanation of the designed ATG algorithm at both high and low levels; and (3) the discussion of the experiment in an emergency response CAE with three generated test scenarios.