"We lost a member of the Dodgers family today. The entire Dodgers organization is mourning the death of John's daughter Christina, and will do everything we can to support John, his wife Roxanna and their son Dallas in the aftermath of this senseless tragedy," said Frank McCourt in a statement.
Her parents said the young girl dreamed of being the first woman to play in Major League Baseball.
Green was attending U.S. Rep. Gabrielle Giffords' meet-and-greet event with a neighbor on Saturday. She wanted to learn more about the political process having been elected to the student council at an elementary school in Arizona.
The 9-year-old was among the 20 people shot in the burst of gunfire outside the Safeway grocery store in Tucson. She was rushed to a local hospital, where she later died.
In a tragic twist, Green was born on 9/11 and was featured as one of 50 children in a book titled "Faces of Hope."
"My daughter was born on a tragic day, and she went out on a tragic day," said her father, John Green.
Her mother, Roxanna Green, said she was a great friend, sister and daughter.
"I was so proud of her," Roxanna Green said. "We got robbed. She got robbed of a beautiful life she could have had."
Green told her parents she wanted to attend Penn State and have a career that involved helping those less fortunate than her.
On Sunday, players from the Dodgers spoke about the tragedy and the loss of the team.
"Any time something tragic like that happens, it affects us because we are a tight-knit group," said Dodgers catcher Griff Erickson. "We are a family, and we're always trying to pull for each other. My heart goes out to [John Green's] family."
Another father grieving is 30-year-old Gabriel Zimmerman, who was Giffords' director of community outreach. He was going to be married in April.
Zimmerman's father, Ross Zimmerman, said he frantically searched for his son after the shooting.
"Nobody could find him, and that's when the horrible realization dawned on us, that they couldn't find him because he wasn't in the emergency room. He had died at the scene, and half of my future is gone," he said.
The fatal victims also included Dorothy Morris, Dorwin Stoddard, Phyllis Scheck and federal judge John Roll.
President Obama was expected to arrive in Tucson for a Wednesday memorial for victims of the shooting.
