In this article, we present a novel plasmonic biosensor, surface plasmon resonance (SPR) sensor, to detect the haemoglobin (HB) in the blood employing the bismuth germanate ( \({\text{Bi}}_{12}{\text{GeO}}_{20}\) ) and bismuth germanium oxide ( \({\text{Bi}}_{4}{{\text{Ge}}_{3}\text{O}}_{12}\) ). The silver (Ag)-based Kretschmann configuration is used to design the proposed sensor to excite the surface plasmons. The sensor’s performance is analysed in terms of sensitivity, quality factor (QF), signal-to-noise ratio (SNR), figure of merit (FoM), and penetration depth using the transfer matrix method with help of angular interrogation technique. The proposed sensor consists of Ag, bismuth germanate and bismuth germanium oxide, and 2D material–based structure. Results declare that the highest attained parameters are a sensitivity of 379.04 \(^\circ /\text{RIU}\) , a QF of 102.26 RIU−1, a FoM of 122.59 RIU−1, and a penetration depth of 165 nm for the proposed sensor. The optimal SPR biosensor have a significant improvement with the existing sensors for rapid and accurate HB detection in a clinical diagnosis. This demonstrates the future integration of new 2D materials with SPR technology for next-generation biomedical sensors in disease diagnosis and health care applications.