Google provides Geocoding/Reverse geocoding API which allow you to get address information from lat/lng.
i.e.) http://maps.googleapis.com/maps/api/geocode/json?latlng=40.714224,-73.961452&sensor=false
In the result, you can find the postal code like this:
More detail, please read the official document. https://developers.google.com/maps/documentation/geocoding/