In neuromorphic photonic systems, device operations are typically governed by analog signals, necessitating digital-to-analog converters (DAC) and analog-to-digital converters (ADC). However, data movement between memory and these converters in conventional von Neumann architectures incur significant energy costs. We propose an analog electronic memory co-located with photonic computing units to eliminate repeated long-distance data movement. Here, we demonstrate a monolithically integrated neuromorphic photonic circuit with on-chip capacitive analog memory and evaluate its performance in machine learning for in situ training and inference using the MNIST dataset. Our analysis shows that integrating analog memory into a neuromorphic photonic architecture can achieve over 26x power savings compared to conventional SRAM-DAC architectures. Furthermore, maintaining a minimum analog memory retention-to-network-latency ratio of 100 maintains >90% inference accuracy, enabling leaky analog memories without substantial performance degradation. This approach reduces reliance on DACs, minimizes data movement, and offers a scalable pathway toward energy-efficient, high-speed neuromorphic photonic computing.