The microwave oven for civilian use was invented in the United States. The first microwave oven called the "Radarange" was introduced by the Raytheon Corporation in 1947. It was the result of a serendipitous discovery by Percy Spencer, an engineer at Raytheon, who noticed that a candy bar in his pocket had melted while he was working with a magnetron (a component used in radar systems) during World War II.
Raytheon developed this accidental discovery into a practical kitchen appliance, and the first commercially available microwave oven, the Radarange, was released for sale in 1947. It was a large and expensive device, and it took a while for microwave ovens to become more compact and affordable for widespread civilian use.
Germany also made significant contributions to the development of microwave technology during World War II, but the first microwave oven specifically for civilian use was indeed invented and commercialized in the United States.