"I don't think so," Green said. "I think I should be good to go before the DL stint is over."
Green hit the game-winning single on Sunday, then tweaked his back doing squats the following afternoon, was unavailable on Monday and Tuesday, "and then I woke up this morning and couldn't stand up straight," he said on Wednesday.
The Angels will continue to rotate left field, first base and DH, with Josh Hamilton and Albert Pujols getting starts at DH as needed, and the left-handed-hitting Efren Navarro and right-handed-hitting Cron probably splitting time filling in.
The Angels have a short bench due to an eight-man bullpen, a situation that is expected to continue at least until Monday's off-day.
Cron, a 24-year-old rookie, batted .295 with nine homers and 27 RBIs in his first 47 games, a big reason why the 42-year-old Raul Ibanez was released. But he went 3-for-26 with seven strikeouts and no walks in his next six contests before being optioned back to the Minors.
Manager Mike Scioscia called it "the cyclical nature of hitting."
"C.J. can hit," Scioscia added. "He's always hit. It's just that there's going to be some periods when you don't get those balls to fall in, and I think more than anything that's what you were seeing with C.J."
Alden Gonzalez is a reporter for MLB.com. Read his blog, Gonzo and "The Show", and follow him on Twitter @Alden_Gonzalez. Matthew DeFranks is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.