No, a zip code is not needed on the wedding invitation for the venue address. Why? Because nothing is being mailed there, and that's what zip codes are for. All you need is the venue name, street address, city and state (spelled out).
Even if you think, "What's the harm in putting it?" you're taking up valuable space on the invitation with unnecessary information. Invitations are for the elegant placement of important information; a perfect example of Less is More.
Any other questions, please don't hesitate to ask!