I upgraded from Mohave to Big Sur and found that homebrew is not working any more. I installed the command line tools using the command
xcode-select --install
When I follow @andrmu instructions, I received an error stating Homebrew: Your CLT does not support macOS 11.0.. I had to first follow the instructions to clean upgrade my command line tools as per the top answer on this issue, then it worked..
Homebrew: Your CLT does not support macOS 11.0.