An increasing number of museum exhibits incorporate multi-modal technologies and interactions; yet these media divert visitors’ attention away from the cultural heritage artifacts on display. This paper proposes an overarching conceptual structure for designing tangible and embodied narrative interaction with cultural heritage artifacts within a museum exhibit so that visitors can interact with them to comprehend their cultural context. The Tangible and Embodied Narrative Framework (TENF) consists of three spectra (diegetic vs. non-diegetic, internal vs. external, and ontological vs. exploratory) and, considering how different interactions map along these three spectra, can guide designers in the way they integrate digital media, narrative, and embodiment. In this paper, we examine interactive narrative scholarship, existing frameworks for tangible and embodied interactions, and tangible and embodied narrative projects. We then describe the design of the TENF and its application to the pilot project, Mapping Place, and to the case study project, Multi-Sensory Prayer Nuts. The findings indicate that embodied engagement with artifacts through a narrative role can help visitors (1) contextualize the meaning of artifacts and (2) make personalized connections to the artifacts. Based on this work, we suggest design recommendations for tailoring the use of the TENF in the cultural heritage domain: simulate cultural practices, associate visitors with cultural perspectives, and provide simultaneous digital feedback. We conclude by describing future directions for the research, which include generating other possible projects using the TENF; collaborating with other designers and museum professionals; and exploring applications of the TENF in museum spaces.