Generally speaking veterans faced the same fate as other German Jews.
Shortly after the Nazi's rise to power they attempted to dismiss, and block from entry, Jews working in state employment. Initially this led to the German President, Paul von Hindenburg, himself a former officer, to petition to Hitler's Chancellery that Jewish veterans should be allowed to remain in their jobs. Hindenburg wrote:
"Recently, a whole series of cases has been reported to me in which judges, lawyers, and officials of the Judiciary who are disabled war veterans and whose record in office is flawless, have been forcibly sent on leave, and are later to be dismissed for the sole reason that they are of Jewish descent...
As far as my own feelings are concerned, officials, judges, teachers and lawyers who are war invalids, fought at the front, are sons of war dead, or themselves lost sons in the war should remain in their positions unless an individual case gives reason for different treatment. If they were worthy of fighting for Germany and bleeding for Germany, then they must also be considered worthy of continuing to serve the Fatherland in their professions."
In his reply, Hitler essentially attempted to justify the dismissal of Jews from state employment as a legitimate act, but also acquiesced to Hindenburg's wishes, at least until his death in 1934, following which the policy was reinstated.
Subsequently Jewish veterans faced broadly the same discrimination and persecution as non-veterans. Under the T4 euthanasia programme and its successors, which forcibly euthanised disabled and mentally ill patients, a number of veterans were murdered. Later, following the outbreak of war many Jewish veterans were sent to either concentration sites, such as the Theresienstadt Ghetto, or to the death camps, where many more were murdered.
During the prewar years a number of Jewish veterans were able to escape from Germany and emigrate abroad. One particular individual who managed to do this, and whose life story is fascinating to discover was Herbert Sulzbach. Sulzbach grew up in Frankfurt before serving as an artillery officer on the Western Front during the First World War, where he won the Iron Cross. In 1937 he emigrated to Britain, and during the Second World War volunteered to join the British Army's Pioneer Corps. Later, Sulzbach was involved in the denazification process of POWs, and went on to win the European Peace Prize in 1978. If you're interested in hearing his life story, you can find an interview with him on the Imperial War Museums website.