"He was OK with me telling everybody what's going on," Francona said. "It's heartbreaking to anyone who has children and I don't even think you need to have children. She's in good hands. She's been getting treatment. She's doing very well. Prognosis is good.
"But, as you can imagine, being a parent, it's pretty tough. Mike understands that he has our blessing to come back and play when he is completely comfortable and wants to and feels like he's where he should be."
Francona noted that the team was informed about the condition of Aviles' daughter during the team's road game against the Royals on Thursday. Aviles was deactivated the following day, but the emergency list only allows players to miss between three to seven days. If Aviles feels he needs more time than that, the Indians would transfer him to MLB's restricted list.
Indians general manager Chris Antonetti indicated that the 34-year-old Aviles might rejoin the Tribe during its upcoming six-game road trip, which begins on Friday in Texas. When Aviles does return, it is possible that he will assume the regular role at shortstop, considering the struggles of Jose Ramirez (.179 average through 24 games).
"Once Aviles gets back," Antonetti said, "that'll continue to provide us a more reliable and veteran Major League player that's had success in that role. Maybe he can absorb a few more of those at-bats and playing time when he returns, which we're hopeful will be at some point on the road trip."
Francona stressed that there is no firm timetable for Aviles' return.
"He may join us this weekend. He may not," Francona said. "It's all dependent on how things are going with him. He's very aware that this cannot be a drag on him, thinking about coming back here. I think it was good for him to come out and see everybody."
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, follow him on Twitter @MLBastian and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.