Advances in technology and an increase in the amount and complexity of data that are generated in healthcare have led to an indispensable revolution in this sector related to big data. Analytics of information based on multimodal clinical data sources requires big data projects. When starting big data projects in the healthcare sector, it is often necessary to assess the maturity of an organization with respect to big data, i.e., its capacity in managing big data. The assessment of the maturity of an organization requires multicriteria decision making as there is no single criterion or dimension that defines the maturity level regarding big data but an entire set of them. Based on the ISO 15504, this article proposes a fuzzy ELECTRE structure methodology to assess the maturity level of small- and medium-sized enterprises in the healthcare sector. The obtained experimental results provide evidence that this methodology helps to determine and compare maturity levels in big data management of organizations or the evolution of maturity over time. This is also useful in terms of diagnosing the readiness of an organization before starting to implement big data initiatives or technologies.