Are migrant entrepreneurs innovative with their business ideas and practices? The introduction of novel business ideas would provide migrant entrepreneurs with a cutting edge advantage against competitors, but the research about this topic is thin on the ground. I propose that the opportunity of migrant entrepreneurs to introduce an innovation is better understood by a closer look at the business idea itself and to which extent it is innovative; by considering the contextual factors where the opportunity structure influences the development of migrant businesses; and by the existence of social connections to share resources and information among entrepreneurs. Such complementary concepts - combining the interaction of the social, human, cultural and financial resources of individual migrants in relation to the wider opportunity structure - provide a comprehensive understanding of the opportunity for entrepreneurs to innovate. By using those contributions as conceptual building blocks, I propose the use of innovativeness levels for migrant entrepreneurs following the processes of adaptation and massification of goods and services introduced by migrants over time. This article builds from existing frameworks: contributions about the definitions and typology of innovation; the mixed-embeddedness approach, which has been largely used to study the opportunity structure; and the model of diffusion of innovations which pays a larger attention to the product and the agency of actors.