Officer Rachel McGuire said Saturday that the woman is recovering.
Tonya Carpenter was struck in the head by the broken bat of former Toronto Blue Jays star Brett Lawrie on Friday night. Carpenter is now in serious condition, her family said in a statement.
"Tonya's family and loved ones are grateful to all who have reached out with thoughts and prayers but are requesting privacy at this time as Tonya recovers," Beth Israel Deaconess Medical Center Hospital said in a statement.
Carpenter had posted a Facebook photo from the game earlier in the evening. A longtime friend, Sheila Hokanson of Charlton, Massachusetts, liked the post and said Carpenter was there with her son and a friend.
"They were just going to a game," Hokanson said in a telephone interview.
"It was just, if you get a chance to get tickets, you grab them and you go and sit where the ticket happens to be," Hokanson said.
There was a moment of reflection for Carpenter at Fenway Park before Saturday's game between the A's and Red Sox. Lawrie was out of the lineup, but manager Bob Melvin said it was because of a back issue, not because of any psychological effects after the incident.
Friday night's game was halted in the second inning as emergency crews tended to a bloodied Carpenter and wheeled her off the field on a stretcher.
Lawrie, who was traded to Oakland in November, broke his bat on a grounder and part of it hurtled a few rows into the seats between the backstop and Oakland's dugout on the third base side.
Alex Merlis, of Brookline, Massachusetts, said he was sitting in the row behind the woman when the broken bat flew into the stands.
"It was violent," he said of the impact to her forehead and top of her head. "She bled a lot. A lot. I don't think I've ever seen anything like that."
There are signs posted on the low retaining wall facing fans in the front row that read: "Be Alert. Foul Balls and Bats Hurt."
Merlis said the woman had been sitting with a small child and a man. After she was injured, the man was tending to her and other people were trying to console the distraught child, he said.
After the game, Lawrie said he hoped the woman would recover.
"I've seen bats fly out of guys' hands in the stands and everyone's OK, but when one breaks like that, has jagged edges on it, anything can happen."
Concerned about a rash of flying broken bats and the danger they posed, Major League Baseball studied the issue in 2008 and implemented a series of changes to bat regulations for the following season.
"I do know that MLB is probably taking a look at the incident last night, as they do with any bat that flies into the stands," Red Sox manager John Farrell said.
Multi-piece bat failures are down about 50 per cent since the beginning of the 2009 season, MLB spokesman Michael Teevan said.
"You have a ballpark here that's how old, and it's close, you have some maple bats that break. I think MLB and the players' association have talked long and hard about how they can try to keep this from happening," Melvin said.
Though dozens of fans at big league ballparks are struck by foul balls each season, there has been only one fatality, according to baseball researchers — a 14-year-old boy killed by a foul line drive off the bat of Manny Mota at Dodger Stadium in 1970.
The National Hockey League ordered safety netting installed at each end of NHL arenas after 13-year-old Brittanie Cecil was killed by a deflected puck at a Columbus Blue Jackets game in 2002. She died two days later, and her parents eventually settled with the team for $1.2 million, the league and the arena management.
AP Baseball Writer Mike Fitzpatrick in New York and Associated Press Writer Kristen De Groot in Philadelphia, and Sylvia Lee Wingfield in Boston contributed to this report.Suggest a correction