Almora -- who has two children -- hit the foul ball in the top of the fourth inning of the 2-1 win on Wednesday at Minute Maid Park in San Francisco. Sources told ESPN and SportsTalk 790 Houston that the little girl's condition was positive.
Javier Baez began the inning with a single, before Astros starter Wade Miley issued a walk to Willson Contreras. Almora then stepped up to the plate. The Cubs outfielder took a called strike and two balls before fouling off Miley's fourth offering of the exchange.
The foul ball fell safely out of play. Almora also fouled off Miley's next offering, but that slice went sizzling into the stands, smacking into a little girl.
Almora was among several players disturbed by the sequence. The Cubs star bent over and hid his face as he shed tears for the child. Almora was embraced by his Cubs teammates and a security guard.
The Astros released a statement, saying the girl was taken to a local hospital. David LeVasseur retrieved the ball after it hit the girl.
"All we heard was screaming," LeVasseur told the Houston Chronicle. "We saw this dad pick up a child and run up the stairs. He took off running. "I [came] upstairs and see the first-aid guys up there and the dad is holding the girl. She [was] alert, she's conscious, she's fine."
"I was just going to give somebody in the family the ball. They kind of, naturally, shook it off. I asked the first-aid guy if she was OK and he said he didn't know."
Several players and analysts called for increased nettings in baseball stadiums around the country following the incident, hoping to prevent future injuries to fans.
"I'm hopeful that I'll have a relationship with that family as long as I'm alive," Almora told reporters.
Almora completed the fourth-inning at-bat with a strikeout. He remained in the game after the scary sequence.