The utilization of natural blue pigments in foods is difficult as they are usually unstable during processing and the commonly applied pH. The current study focuses on natural blue pigment, possessing antioxidant properties, found in Arthrospira platensis (spirulina), and phycobiliproteins (PBP). These pigments are a complex of conjugated protein and non-protein components, known as phycocyanobilin. PBP has low stability during pasteurization (high-pressure or heat treatments), resulting in protein denaturation and color deterioration that limits the application. The phycocyanobilin pigment might also be liable to oxidation during pasteurization and storage, resulting in color deterioration. Yet, the instability of the pigment phycocyanobilin during the pasteurization process and storage conditions was never studied before, limiting the comprehensive understanding of the reasons for PBP instability. In this study, the stability of phycocyanobilin under high-pressure and high-temperature conditions was compared to the stability of phycobiliproteins. We revealed that phycobiliproteins have a higher color deterioration rate at 70–80 °C than at high-pressure (300–600 MPa) whereas phycocyanobilin remained stable during high-pressure and heat processing. During storage at pH 7, phycocyanobilin was oxidized, and the oxidation rate increased with increasing pH, while at lower pH phycocyanobilin had low solubility and resulted in aggregation.