The Soup Nazi, one of Seinfeld’s most beloved characters, closes up shop and moves to Argentina! The stone-faced tyrannical soup dictator is based on real life New York City soup man extraordinaire, with quite an interesting backstory. Al Yeganeh ran Soup Kitchen International in Manhattan. He served deliciously flavorful soups that kept clients coming back for more despite his harsh personality and hostile interactions with customers. While customers did not identify him as the Soup Nazi, they did adopt the nickname “The Terrorist.” With no rhyme or reason to his authoritative rule, some lucky ones were given extra bread and some kicked out by not following his rules (like George).
My favorite part of this backstory is after the episode aired, Jerry Seinfeld and some other writers went to order lunch from Yeganeh. Upon sight of Seinfeld and crew, Yeganeh exploded in an incredible rage, shouting vulgar profanities at Seinfeld because, as he claimed, the character depicted on the show “ruined his life” and demanded an apology from Seinfeld. In Season 7 on the DVD bonus materials, writer of the episode Spike Feresten, who went to the soup stand with Seinfeld for lunch, recounts the story and describes the apology Seinfeld gave as “the most sarcastic, insincere apology” he’d ever heard. What came next couldn’t be more perfect, as if the cameras were rolling and it was part of a Seinfeld script… Yeganeh, in a fury, screams “No soup for you!” expelling Seinfeld and friends from the restaurant.
Back to the Argentina connection: Sure Argentina has a long history of Nazis allegedly escaping and hiding out in Argentina. But apparently, the NYC store closed down one summer, and a sign on the door was posted notifying the public that the chef would be in Argentina. Writers took this and ran with it, like many of Seinfeld’s supporting characters and side stories.
Source & Seinfeld Season 7 DVD
¿Qué Sé Yo, Argentina? 
After world war II, Argentina was the refuge for thousands of Nazis fleeing occupied Germany, and I thought the Soup Nazi “moving to Argentina” line was a clever reference to that.
I thought so too until reading this article. I guess it’s a two level joke to those knew of Yeganeh and those smart enough to make the connection you did. In any case, the person in charge of prompting the audience to laugh (or just pressing the ‘canned laughter’ button) didn’t get either of the two connotations!