The 25-year-old right-hander has allowed two runs in 9 1/3 innings (1.93 ERA) spanning three spring appearances (two starts). He has scattered seven hits and walked two batters, striking out 10.
Girardi said that while Tanaka makes the 2 1/2-hour trip to Fort Myers, right-hander Hiroki Kuroda will stay back in Tampa to pitch in a Minor League game.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.