She was transported to nearby NewYork-Presbyterian/Columbia University Medical Center.
Her father and grandfather spoke briefly with reporters there Wednesday night. When asked whether she would need surgery, the girl's father, who declined to give his name, said: "It's too early to tell."
"She's doing all right. Just keep her in your thoughts," he told WABC-NY.
The toddler was attending the game with her grandparents.
The Yankees declined to talk about her status, citing HIPAA laws that protect individuals' privacy. During Yankees manager Joe Girardi's postgame news conference, he said he was told by members of the team's security staff that the girl was doing OK, but he said that was only secondhand or thirdhand information.
Frazier had tears in his eyes as he spoke to reporters after the game. It was his fifth-inning liner that hit the girl in the face as she sat with her grandparents about five rows up on the third-base side of Yankee Stadium. Frazier said he thought of his own two children, who are both under 3 years old.
"It was terrible," Frazier said. "I was shaken up a little bit. I hope she is all right. It is something that I wish never happened. It was tough. Tough to watch. Tough to be a part of, to be honest."
The protective netting at Yankee Stadium ends at the home plate side of each dugout. After the game, many players voiced support for more safeguards.
"We need it," Yankees All-Star Aaron Judge said.
Twins second baseman Brian Dozier offered his impressions.
"Either, one, you don't bring kids down there, or No. 2, every stadium needs to have nets," Dozier said. "That's it. I don't care about the damn view of a fan or what. It's all about safety.
"I still have a knot in my stomach. ... I hope the kid's OK. We need nets, or don't put kids down there."
Major League Baseball issued recommendations for protective netting or screens in December 2015, encouraging teams to have it in place between the ends of the dugouts closest to home plate.
"It remains an ongoing discussion in the industry,'' commissioner Rob Manfred said at Safeco Field before Wednesday night's game between the Seattle Mariners and Texas Rangers. "We gave some guidelines two years ago, and what we have done since then is that we have encouraged the individual clubs to engage in a localized process, look at their own stadiums -- every stadium's different -- and to try to make a good decision about how far the netting should go in order to promote fan safety.
"If you look at what's happened, there has been a continuous focus-forward movement in terms of increased netting in stadiums around the leagues, and I expect that process will continue this offseason."
On Thursday, Manfred told ESPN's Bob Ley through a spokesman that the league would "redouble" its efforts to promote expanded netting following Wednesday's incident.
The Yankees have been examining the issue, which has been pushed to the forefront by New York City Council member Rafael L. Espinal Jr., who introduced legislation in May that city ballparks should extend their netting to protect fans.
The New York Mets already have made adjustments to Citi Field, extending netting beyond the outfield ends of the dugouts this season following the All-Star break.
"No one should ever go to a baseball game and leave severely injured," Espinal said in a statement Wednesday. "Nor should any player have to feel the guilt associated with injuring a fan, especially when that injury could have been prevented by safety nets. Since introducing this legislation, I have been in contact with both teams, and I commend the Mets for stepping to the plate and leading the country by extending their netting farther than any other team. Since then, we have been waiting to hear from the Yankees on their plans on how they will move forward and urge them to let the public know as soon as possible where they stand."
Over the summer, the Yankees said they were "seriously exploring" extending the netting for 2018. A team spokesman said the Yankees had no comment or update on where those plans stood.
On Wednesday, players from the Yankees and Twins wished the netting already had been extended after they saw the girl struck.
"Our players were very disturbed," Girardi said. "I was at Wrigley Field as a player and saw a young man get hit. And I think that he was in a coma for a day or two. And I was catching that game, and it really stuck with me.
"Does it happen more now? I don't know. I do think the fans are closer to the home plate now, and that might need to be something that needs to be evaluated."
Information from The Associated Press was used in this report.