Okajima, 36, had signed a Minor League contract with a spring invitation in late December, hoping to bounce back to the effective form he showed in his first few seasons with the Red Sox.
WFAN 660 AM in New York first reported on Friday that Okajima would not be in camp.
The Yankees had interest in Okajima as a left-handed specialist to help out behind Boone Logan in their bullpen, casting a wide net of low-risk players to evaluate in the spring.
Okajima fell out of favor with the Red Sox and spent most of last season at Triple-A Pawtucket, limited to seven big league outings in April and May, when he was 1-0 with a 4.32 ERA in 8 1/3 innings.
The Red Sox did not recall Okajima when rosters expanded in September, despite a 2.29 ERA in 34 appearances at Triple-A, spanning 51 innings.
Okajima came to the Major Leagues in 2007 after pitching with the Yomiuri Giants and Hokkaido Nippon Ham Fighters in Japan. He compiled a big league record of 17-8 with six saves and a 3.11 ERA in 261 appearances with Boston, holding left-handed batters to a .218 batting average.
New York also traded up to select another Red Sox left-hander in the Rule 5 Draft in December, acquiring 22-year-old Cesar Cabral from the Royals in exchange for cash considerations.
Cabral, who was a standout in the Dominican Winter League with Aguilas, could now see improvement in his chances of sticking on the roster. The Yankees have also invited lefty relievers Juan Cedeno and Mike O'Connor to camp.