No, General Eric K. Shinseki is not a Jew.
President-Elect Obama has nominated this Asian-American to the post of Veterans Affairs secretary adding to the diverse character of his proposed cabinet. Shinseki was born to a Japanese American family in Hawaii.
The AP observes, "In Obama's eight Cabinet announcements so far, white men are the minority with two nominations — Timothy Geithner at Treasury and Robert Gates at Defense. Three are women — Janet Napolitano at Homeland Security, Susan Rice as United Nations ambassador and Hillary Rodham Clinton at State. Eric Holder at the Justice Department is African American, while Bill Richardson at Commerce is Latino."
In fact, none of these nominees to the cabinet is Jewish. Several of Obama's proposed White House staff members are Jewish.