Were any American generals captured by the Germans during World War 2?

Yes. There was Brig. Gen. Arthur Vanaman. He was shot down in June 1944 under odd circumstances and eventually was sent to Stalag Luft III, famous as the site of the Great Escape although Vanaman got there four months later. Maj. General Maurice Rose, CO of the 3rd Armored Division, was captured very late in the war, on March 30, 1945. As he was reaching into his jacket, presumably to surrender his personal sidearm, he was gunned down by a German tank commander. He was a prisoner for just a few seconds before being killed. The Japanese captured at least four generals (Wainwright, King, Fort, and Lim), all in the Phillippines in 1942, and executed the latter two.