The 2-year-old girl stayed in the hospital overnight for observation but is expected to be OK.
"She's doing all right, just keep her in your thoughts," the victim's father said.
A 105 mile-an-hour foul ball went off the bat of Todd Frazier and hit the little girl in the face during the game between the Yankees and the Minnesota Twins.
The game was delayed for about 4 minutes while she was attended to and then carried from the seats in the bottom of the fifth inning.
PHOTOS: Young fan struck by ball at Yankees game
Fans frantically waved for help and players were distraught, some with tears in their eyes.
Here's video showing the reaction on the field:
Frazier, crouched over with his hands over his face.
"I thought of my kids. I have two kids under 3 years old, and I just hope she's alright," Frazier said.
After Wednesday's incident several players are now coming out in favor of that netting.
Asked whether there should be more netting, Yankees rookie slugger Aaron Judge said: "We need it."
Twins players also were distressed, and second baseman Brian Dozier and the Yankees' Matt Holliday had tears as they said prayers at second base.
"We've been trying to get these teams to put nets up," Dozier said. "Number one, you don't bring kids down there. And number two, every stadium needs to have nets. That's it. I don't care about the damn view of the fan or what. It's all about safety. I still have a knot in my stomach."
As to what it would take to get nets up, Dozier responded: "The last resort that we don't ever want to have happen. I'm not going to say it, but you know what I'm talking about."
The Mets extended the netting at Citi Field this season.
New York City Councilmember Rafael Espinal has introduced legislation to turn that recommendation into city law to protect fans.
"They shouldn't be worried about getting injured. That shouldn't be on the back of their minds," Councilmember Espinal said. "What they should be worrying about is having a good time with their families, eating a hot dog, watching their favorite players out on the field."
Major League Baseball issued recommendations for protecting 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 Seattle and Texas. "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," he said.
(The Associated Press contributed to this report.)