Beckham has been battling a sore hand since Aug. 30 at Cleveland when he was hit by a pitch. Since then, he has developed a cut between his right thumb and index finger that he said was caused by a wrap he used to "keep the pressure off" his hand.
"It just kind of developed," Beckham said.
White Sox manager Ozzie Guillen said he expects Beckham to be back in the lineup soon, but he wants to see proof first that he's ready to play.
"Last time he did it -- 'I'm ready, I'm fine, I'm cool' -- he missed a few days because we believed he was fine, but he wasn't," Guillen said.
Beckham has hit .310 since the All-Star break and has raised his average to .252. But he has just three hits in his past 21 at-bats and has no homers and just one extra-base hit since his injury.
"I don't know how many at-bats I've had this month, but ... I've been pretty hurt in those at-bats, so in a way I gave them away," Beckham said. "I brought the average down a little bit. I'm just trying to get out there and play and help the team.
"If I can be out there, I'm going to do it. It's frustrating I got hit there. I've never been without the use of my hands. I think they're one of my best attributes. It's been difficult to get through this, but you've got to play through it sometimes."
Whatever happens the rest of the season, Beckham will go into the offseason knowing he rebounded from a rough first half of the season.
"Yeah, I came back," Beckham said. "I came back from a real tough time in my baseball career. It's always nice to show that you can respond and come back from it, even when you feel like there's no chance you can do it."