Carpenter had been in serious condition throughout the weekend. The family has remained by her side and has requested privacy as she recovers.
Carpenter was injured during the second inning of Friday's game when Oakland third baseman Brett Lawrie's shattered bat went flying into the seats behind the A's on-deck circle. She was admitted to Beth Israel Deaconess Medical Center with life-threatening injuries after receiving first aid at Fenway.
On Monday, Major League Baseball Commissioner Rob Manfred told reporters at the 2015 MLB Draft that the league plans on taking a fresh look at the state of fan safety at games.
"First and most important thing to say is, we're all concerned about the long-term well being about the woman who was injured," Manfred said. "From Major League Baseball's perspective, when you have an incident like this, you have to go back and re-evaluate where you are on all of your safety issues. Trust me, we will do that.
"It's important not to lose sight of the fact that we have taken important steps in this area. Bat safety is much improved from where it was a few years ago. We've spent a lot of time, effort and money to make sure that our bats are safer and we have less of these incidents.
"You have to react strongly to an incident like this. But I think the best word for this is, we're going to re-evaluate where we are on the topic."
When asked if more netting might be installed at Fenway Park, if not other parks, Manfred said any discussions would be threefold, including clubs and the MLB Players Association.
"There are a variety of issues that we're going to take a fresh look at," Manfred said. "Some of the changes would affect play on the field, and the MLBPA might be involved in those discussions, and then obviously us and the clubs. This is an important issue, and as with all topics, we want to make sure we know where our clubs are on a topic."
The Red Sox shared similar sentiments in a statement released Monday night:
"All of us with the Boston Red Sox continue to extend our best wishes to Tonya Carpenter, who was injured by a broken bat at Friday night's game," the statement read. "The well-being of Tonya and her loved ones are forefront in our minds.
"Major League Baseball will re-examine fan safety at ballparks, and we will fully participate in that process."
The Red Sox held a moment of reflection for Carpenter before Saturday's game at Fenway.
"I got sick," Boston left fielder Hanley Ramirez said on Saturday. "It's bad. I couldn't sleep last night. I went to bed late. I actually posted something on Instagram. Everybody just pray. It's not good. Hopefully she gets back and feels better."
A's manager Bob Melvin said Lawrie's thoughts have been with the fan in the days following the accident. Lawrie reportedly sent flowers and a card to Carpenter in the hospital.
"Do the best you can with it," Melvin said on Sunday. "It's a sad situation. There's nothing he could have done about it. Just say your prayers. You still have a job to do out here, but I know he thinks about it quite a bit."
The Red Sox issued the following statement on Saturday: "A woman was injured by a broken bat that flew into the stands in the top of the second inning of last night's game. The fan was immediately transported to Beth Israel Deaconess Medical Center, where she is being treated. All of us offer our prayers and our thoughts as we wish her a speedy recovery."
MLB released the following statement: "We will continue to keep her and her family in our thoughts and prayers. We appreciate the efforts of the Red Sox, the first responders, the Boston Police Department and Beth Israel Deaconess Medical Center. Fan safety is our foremost goal for all those who choose to support our game by visiting our ballparks, and we will always strive for that experience to be safe and fan-friendly."