I ran across this question while personally researching the history of American cheese (as one does), and I found sporadic records referencing this event.
As I am able to find, the OPA (Office of Price Administration) was responsible for administrating rationing by civilians during World War 2. Allegedly, The OPA created the restriction on non-american cheeses and cited two reasons: First that it was necessary to promote patriotism through consumption of domestic products and second that it was necessary as a response to wartime trade disruptions causing a lack of export of American cheese and lack of import of European cheeses. Then, only 3 months later, the restriction was lifted in response to US cheese importers lobbying against the ban, claiming it disrupted both their business and American solidarity with our European allies.
Due to the age, brevity, and esoteric nature of the problem, I am unable to locate any official document or even a witness account of the event. I was however able to find several references to the existence of the restriction.
The first reference I found regarding restriction is in the book "For the Duration ...: The United States Goes to War, Pearl Harbor-1942" by Kennet Lee
There is some account also in the book "Paradox of Plenty: A social History of Eating in Modern America" by Harvey Levenstein
Both Lee and Levenstein give all of 2 sentences on the matter and do not cite sources.
There is a mention of the rescinding of the restriction as it was deemed lacking in solidarity with our European allies in "Food and Conflict in Europe in the Age of the Two World Wars" by Frank Trentmann and Flemming Just.
I suspect that if this event occurred, I would be more well known and that I would be able to find better sources. Thanks if anyone has more definite answers.
To clairify, this potentially meant cheese made in the USA, not necessarily the Kraft singles we know as "American cheese" today. As I understand, the phrase "American cheese" was used to refer to either in that era.
As you said in this case "American Cheese" has potentially two meanings. The real question is if the original wording of the OPA's regulation was "American cheese" or "domestic cheese" (or something similar to the latter).
The reason it matters is because the name American Cheese, even in the period around WWII, most typically meant Kraft singles. The development of American cheese was something that happened early in the 20th century, well before WWII, and the name "American cheese" was already widespread throughout the country to refer to this kind of cheese, of which Kraft was the most well known producer and originator, but not the only one. Of course for it to matter to this particular question the ban would have to be legitimate.
So then as for the rationing and restriction to only American cheeses (one version) or specifically Kraft singles (another version, as popularly described on various low-effort food history sites), it supposedly lasted from 4th May 1942 until 1st August of the same year. That start day should be familiar to anyone who's looked into rationing before since it's the date the OPA first issued their rationing books. The thing is, there's no clear indication of either a cheese-specific limitation, nor the cancellation of the restriction in August. Newspapers from the period make no mention of it, as far as I've been able to dig up, and various sources throughout the period are still talking about imported cheeses.
Anyway, the idea that the only permissible cheese was American cheese in the Kraft singles sense is unquestionably not true. There is no shortage of advertisements for other cheeses being run in magazines like LIFE throughout the supposed ban period, and cottage cheese is again and again recommended in newspapers and magazines during those three months. That's not the case later, though, as later rationing is much more visible even before the fact (1943's rationing), as was any change in the restrictions (1944).
It seems that the idea of a ban is at best the result of a misunderstanding that has snowballed as blog after blog has parroted those that came before it, adding details or making minor changes to the story until it sounds completely believable. Pop food sites then pick it up and now it's "fact".
If the ban was ever actually attempted, no one was talking about it and it doesn't seem like it was in any way enforced. Later, the following year, cheese was added to the list of rationed goods. But the notion of it's
That's not to say Americans were chowing down on Roquefort and Gruyère during those months. Most of the major cheese producing countries were undergoing the same sorts of rationing, and exports were quite low in most parts of the Old World. This was actually good news (literally, e.g. Cheese Outlook Bright from November 1942) as it gave an extra push to US production.
Finally, even if imports were restricted, it would likely not have made a dent in consumption. There was a shortage of storage for dairy goods at the time given the cast amount of cheese being produced domestically, as well as the various imported dairy products that continued to arrive in the middle of the year from other countries, and once cheese and meat were rationed, there was an active black market (called the "Red Market" since it was the red ration stamps that covered meat and cheese, blue for canned goods) in cheese sales, and the people who could afford to eat it continued to eat eat.
That said, if you're in the US and are up for a field trip, there's always the National Archives. They have records of their records of the Office of Price Administration for the 1940s available here, which includes records of the Rationing Department from 1940 to 1947. Unfortunately those aren't scanned documents, but instead just listings of where you can read them, which is why the field trip is necessary. You'd need to drive out to one of the places where the documents are stored.