Ramirez did not start Sunday and is hitless in his past four games. He's batting .160 overall.
"I'm sure the discomfort in his hand hasn't helped," Cubs manager Lou Piniella said.
There's been no talk about putting Ramirez on the disabled list.
"We haven't discussed that," Piniella said. "If he's going to be out for an extended period of time, that might change."
Jeff Baker started at third base on Tuesday against the Dodgers and lefty Clayton Kershaw.