For some reason there is no way (as of the date of this writing) to right click, zip and password protect a file in OSX. So we have to go to the Terminal app, or my preference - iTerm2.

I like to launch pretty much everything in OSX by using the shortcut/hotkey: Command + Space bar. This will open the Spotlight Search bar for you. Type “Terminal” in Spotlight, then double-click on Terminal (or select it and press the enter key) to open it. Alternatively, you can go to Finder, scroll down to “Utilities,” and then select “Terminal” from the Utilities programs folder.

In the Terminal window you'll have to navigate to the location of the file you want to zip. Once there type:

zip –e name_of_zip_file_to_create name_of_file_to_zip

The “-e” flag means create an encrypted zip file.
The first file name is what you want the zipped file to be called.
The second file name is the folder or file you want to zip.

Example

Erics-MBP:~ ewilson$ cd Desktop/
Erics-MBP:Desktop ewilson$ zip -e wilson.zip wilson.pdf
Enter password:
Verify password:
adding: wilson.pdf (deflated 4%)

As you can see the archive utility will ask you to enter a password twice. Complete this step and you'll have successfully password protected you zip file.