The game was delayed for several minutes while Ramirez was treated for the injury, which occurred while trying to barehand a slow grounder.
The finger remained wrapped up in the locker room before Tuesday's game and Ramirez was ready to try again.
"If I would say it's not hurting me, I'd be lying," he said through an interpreter.
White Sox manager Robin Ventura said the biggest problem might be swinging a bat, which could bring the shortstop some pain.
"Every once in a while it will bite him a little," Ventura said."He can throw. It may [bother him more] hitting. I think the more he does it, we'll find out for sure."