What are the minimum hardware requirements to run an EOS blockchain in terms of CPU power, RAM, etc?
EOSIO can run with very little memory, less than 100MB + shared memory file size. The requirements for the shared memory file depends upon the state of your local application (number of users, etc).
I was able to run Single Node Testnet on Ubuntu using Docker on my machine with around 2GB RAM without problem (as bytemaster said it requires little memory actually).
The CPU and Disk Space are not mentioned explicitly. I guess you will need decent disk space once the blockchain increases in size. Also, probably it's good idea to compare the hardware specifications of the current block producers.
In case you want to build it natively you can find the requirements on their official Wiki (thanks John Haager for clarification)
You can build and run with as little as 2 Cores and 4GB of RAM: