Carter, 28, was one of the Padres' primary Minor League free-agent targets in the offseason after he posted a 3.47 ERA and 79 strikeouts in 62 1/3 innings with Boston's Triple-A affiliate in Pawtucket.
But Carter failed to impress in big league camp during Spring Training, allowing seven earned runs on 11 hits in five innings (six outings) before being reassigned to Minor League camp on March 15.
Carter appeared in three games for the Triple-A Chihuahuas, allowing two runs on five hits in three innings. He last appeared in a game on April 9.
"He had interest in going over to Japan prior to us signing him," said Padres assistant general manager A.J. Hinch. "They showed interest, and we matched it up against our depth and felt it would be mutually beneficial."
The Padres have had a working agreement with the Fighters since 2008, though they're free to deal with other Japanese teams; in January '13, they sold the contract of first baseman Matt Clark to the Chunichi Dragons.