The ball was hit down the third-base line off the bat of Todd Frazier and stuck the fan in the stands.
The girl is a toddler and was hit on the face, a source told ESPN's Andrew Marchand. She was taken to Columbia Presbyterian Hospital.
PHOTOS: Girl struck by ball at Yankees game
The girl was carried out of the stands, given first aid and taken to a hospital. The protective netting at Yankee Stadium ends at the home plate side of each dugout, and the team said in July it is "seriously exploring" extending the netting for 2018.
Frazier knelt down and covered his head, and many other Yankees and Twins watched in stunned silence as the fan was helped.
Here's video showing the reaction on the field:
The Yankees said they weren't allowed to provide more information on her condition, though they provided a statement:
"The child who was struck with a batted ball today was given first aid at the ballpark and is receiving medical attention at an area hospital. The federal Health Insurance Portability and Accountability Act, known as HIPAA, prevents the team from giving more information. We will have no further comment at this time."
The game was briefly halted while crews helped the young girl.
The Associated Press and ESPN contributed to this story.