With an ongoing trend in computing hardware toward increased heterogeneity, domain-specific coprocessors are emerging as alternatives to centralized paradigms. The tensor core unit has been shown to outperform graphic processing units by almost 3 orders of magnitude, enabled by a stronger signal and greater energy efficiency. In this context, photons bear several synergistic physical properties while phase-change materials allow for local nonvolatile mnemonic functionality in these emerging distributed non-von Neumann architectures. While several photonic neural network designs have been explored, a photonic tensor core to perform tensor operations is yet to be implemented. In this manuscript, we introduce an integrated photonics-based tensor core unit by strategically utilizing (i) photonic parallelism via wavelength division multiplexing, (ii) high 2 peta-operations-per-second throughputs enabled by tens of picosecond-short delays from optoelectronics and compact photonic integrated circuitry, and (iii) near-zero static power-consuming novel photonic multi-state memories based on phase-change materials featuring vanishing losses in the amorphous state. Combining these physical synergies of material, function, and system, we show, supported by numerical simulations, that the performance of this 4-bit photonic tensor core unit can be 1 order of magnitude higher for electrical data. The full potential of this photonic tensor processor is delivered for optical data being processed, where we find a 2–3 orders higher performance (operations per joule), as compared to an electrical tensor core unit, while featuring similar chip areas. This work shows that photonic specialized processors have the potential to augment electronic systems and may perform exceptionally well in network-edge devices in the looming 5G networks and beyond.