Due to its promising performance, deep hashing has become a prevalent method for approximate nearest neighbors search (ANNs). However, most of current deep hashing methods are validated on relatively small-scale datasets, leaving potential threats when are applied to large-scale real-world scenarios. Specifically, they can be constrained either by the computational cost due to the large number of training categories and samples, or unsatisfactory accuracy. To tackle those issues, we propose a novel deep hashing framework based on product quantization (PQ). It uses a softmax-based differentiable PQ branch to learn a set of predefined PQ codes of the classes. Our method is easy to implement, does not involve large-scale matrix operations, and learns highly discriminate compact codes. We validate our method on multiple large-scaled datasets, including ImageNet100, ImageNet1K, and Glint360K, where the category size scales from 100 to 360K and sample number scales from 10K to 17 million, respectively. Extensive experiments demonstrate the superiority of our method. Code is available at https://github.com/yuleung/FPPQ.