On-chip power meters play a critical role in power management by generating timely and accurate power traces at runtime. However, both performance-counter-based and existing RTL-based on-chip power meters have difficulty in providing sufficient response time for fast power and voltage management scenarios. Additionally, they can be costly to implement for large-scale DNN accelerators with many homogeneous process elements. To address these limitations, this paper proposes PROPHET, a data-pattern-based predictive on-chip power meter targeting multiply-accumulate-based DNN accelerators. By sampling pre-defined data patterns during memory access, PROPHET can predict power consumption before it actually happens. In our experiments, PROPHET predicts power consumption dozens of clock cycles in advance, with a temporal resolution of 4 clock cycles and NMAE < 7% and area overhead < 2% for various systolic-array-based DNN accelerators. PROPHET has the potential to enable fine-grained power management and optimization for large-scale DNN accelerators, improving their energy efficiency.