Yes, it’s called ~/.zshenv.
Here’s how I have $JAVA_HOME set in ~/.zshenv:
export JAVA_HOME="$(/usr/libexec/java_home)"
Keep in mind, however, that zsh is not bash, so just ’cause you have to source your .bash_profile every time you open a terminal does not mean that you have to do that with zsh. With zsh, I only have to re-source my ~/.zshenv when I make changes to it, and then only for terminals which are already open: new terminals should have already sourced my new and improved ~/.zshenv.
NOTE
I often find it helpful, when trying to determine which of my zsh startup files I should place things in to consult zsh startup files.
A newer version of the documentation for startup files can be found here.