e.g.,
$ echo $PATH
/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin:/usr/local/bin:/bin:~/bin:/usr/local/Cellar/python3/3.2.3/bin
$ vim
:! echo $PATH
/usr/bin:/bin
There are many similar questions on stackoverflow and stackexchange.
Your shell executes different *rc files depending on the arguments its given at launch time. Therefore, you need to setup Vim so that it launchs your shell with the right arguments.
The following helps in bash, I'm almost certain there's a similar flag in zsh.
set shell=bash\ -i
See $ man zsh
for the right flag and the right execution order.