Biomedical engineering involves ideologies and problem-solving methods of engineering to biology and medicine. Malaria is a life-threatening illness, which has gained significant attention among researchers. Since the manual diagnosis of malaria in a clinical setting is tedious, automated tools based on computational intelligence (CI) tools have gained considerable interest. Though earlier studies were focused on the handcrafted features, the diagnostic accuracy can be boosted through deep learning (DL) methods. This study introduces a new Barnacles Mating Optimizer with Deep Transfer Learning Enabled Biomedical Malaria Parasite Detection and Classification (BMODTL-BMPC) model. The presented BMODTL-BMPC model involves the design of intelligent models for the recognition and classification of malaria parasites. Initially, the Gaussian filtering (GF) approach is employed to eradicate noise in blood smear images. Then, Graph cuts (GC) segmentation technique is applied to determine the affected regions in the blood smear images. Moreover, the barnacles mating optimizer (BMO) algorithm with the NasNetLarge model is employed for the feature extraction process. Furthermore, the extreme learning machine (ELM) classification model is employed for the identification and classification of malaria parasites. To assure the enhanced outcomes of the BMODTL-BMPC technique, a wide-ranging experimentation analysis is performed using a benchmark dataset. The experimental results show that the BMODTL-BMPC technique outperforms other recent approaches.