Cabrera tweaked his right leg while stealing second base in the eighth inning of Monday's 3-2 win over Chicago.
Mike Aviles started in place of Cabrera at shortstop on Wednesday.
"He was running the bases and he felt his quad a little bit," Francona said of Cabrera. "We're just going to try to take advantage. It's a miserable day and we have the day off [Thursday]. We lean on him pretty hard. So we'll give him a day, let Aviles play short and let [Cabrera] come in Friday feeling really good."
Santana has felt ill for the past couple of days. The Indians catcher saw a doctor in Chicago on Tuesday night and was given medication.
"He's a little bit enfermo," Francona said. "They've got him on meds and everything. We'll get him feeling better and hopefully not have him get everybody else sick. He can be our backup in case something happens. He's just not feeling well."
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.