Advancements in healthcare industry with new technology and population growth has given rise to security threat to our most personal data. The healthcare data management system consists of records in different formats such as text, numeric, pictures and videos leading to data which is big and unstructured. Also, hospitals have several branches at different locations throughout a country and overseas. In view of these requirements a cloud based healthcare management system can be an effective solution for efficient health care data management. One of the major concerns of a cloud based healthcare system is the security aspect. It includes theft to identity, tax fraudulence, insurance frauds, medical frauds and defamation of high profile patients. Hence, a secure data access and retrieval is needed in order to provide security of critical medical records in health care management system. Biometric authentication mechanism is suitable in this scenario since it overcomes the limitations of token theft and forgetting passwords in conventional token id-password mechanism used for providing security. It also has high accuracy rate for secure data access and retrieval. In this paper we propose BAMHealthCloud which is a cloud based system for management of healthcare data, it ensures security of data through biometric authentication. It has been developed after performing a detailed case study on healthcare sector in a developing country. Training of the signature samples for authentication purpose has been performed in parallel on hadoop MapReduce framework using Resilient Backpropagation neural network. From rigorous experiments it can be concluded that it achieves a speedup of 9x, Equal error rate (EER) of 0.12, sensitivity of 0.98 and specificity of 0.95 as compared to other approaches existing in literature.