Looks like we have conflicting sources:
In May 1940, Greenberg's baseball career was interrupted when he was drafted into the Army. One of baseball's highest paid stars, his salary dropped from $11,000 to $21 per month. In August, Congress decided that men over 28 years old need not serve, and Greenberg was honorably discharged. He planned to return to the Tigers the next season, but on December 7, 1941, the Japanese bombed Pearl Harbor and the U.S. declared war. Greenberg was the first major leaguer to enlist in the Army, even though he had been excused from serving. While he could have had a stateside job as an athletic instructor, Greenberg chose to serve in the Army Air Corps in the China Burma-India Theater, where he had a distinguished record.
http://www.jewishvirtuallibrary.org/...greenberg.html