Testing safety-critical systems is crucial since a failure or malfunction may result in death or serious injuries to people, equipment, or environment. An important challenge in testing is the derivation of test cases that can identify the potential faults. Model-based testing adopts models of a system under test and/or its environment to derive test artifacts. This paper aims to provide a systematic mapping study to identify, analyze, and describe the state-of-the-art advances in model-based testing for software safety. The systematic mapping study is conducted as a multi-phase study selection process using the published literature in major software engineering journals and conference proceedings. We reviewed 751 papers and 36 of them have been selected as primary studies to answer our research questions. Based on the analysis of the data extraction process, we discuss the primary trends and approaches and present the identified obstacles. This study shows that model-based testing can provide important benefits for software safety testing. Several solution directions have been identified, but further research is critical for reliable model-based testing approach for safety.