A woman walking her dog in the Neve Yaakov area first alerted the authorities after finding signs of an archaeological dig near her home.
Members of the authority, surprised to hear about an excavation they did not know about, chanced upon the young archaeology buff who explained that he had organised the dig with friends.
He discovered the wine press, estimated to date back nearly two and a half millennia and measuring some five metres (16 feet) by five metres.
He said the youthful amateurs had now been invited to take part in authorised digs monitored by professionals.