The 31-year-old hit just .229 with a .275 on-base percentage in 19 Cactus League games.
An All-Star and Gold Glove winner with the Nippon Ham Fighters in Japan, he committed seven errors attempting to play shortstop and third base this spring.
"He's one of the hardest workers you'll see," Giants manager Bruce Bochy said. "But coming here is an adjustment for him. He's had a lot on his plate, trying to play short and third."
Tanaka had been in contention with Wilson Valdez and Tony Abreu to take the backup utility role behind Joaquin Arias following the departures of Ryan Theriot and Emmanuel Burriss.
With Tanaka gone and Abreu hurt, the less than impressive Valdez has a better chance to make the Opening Day roster, but the Giants will continue to look for other infield options.
Tanaka is scheduled to report to the Grizzlies camp on Friday.
Giants fans should still expect to see him in the majors sometime this year.
Catchers Johnny Monell and Jackson Williams were also sent to Minor League camp Thursday.