There are no official static minimum requirements for running a block producing node, but nodeos
installation requires 8GB of RAM by default.
The available RAM of the network increases every block, and the network latency and processing speeds for various BPs vary significantly. In order to produce blocks, a node should be capable of staying synchronized with the rest of the network, which entails being able to process all blocks to derive the state and communicating the blocks timely. If, for instance, most BPs use highly performant machines, a less performant machine may not be able to process the transactions in the blocks at the speed at which they are produced, meaning they'll never be in synch or produce blocks in the consensus chain.
Thus, the technical requirements of being an active BP are perpetually changing and dictated by the other BPs. In an older answer, I compiled several resources that aim to showcase the technical resources of various BPs here, but please note that it is not possible to verify that the advertised specs are actually used, and the only practical way to validate performance is empirically through analyzing BP performance (websites that monitor BP performance). As such, to be safe, one would expect that their hardware must be at least as good as the least performing BP in order to stay synchronized, so verifying their performance and advertised specs should provide an approximation of what is required at any time.
For reference, one could check, for instance, the technical setup claimeddescribed by EOS New York as it's one of the BPs that has been active since launch. Excerpt:
Core Layer
One producing node and multiple fully redundant backups in a fail-over model comprise our core layer. The main producing node is the workhorse of the operation. A backup is activated during system upgrades.
80 GBs - 3 TBs of RAM (as needed)
4-8 vCPUs
1 TB of SSD Storage