On Facebook, Fort Ben County Sheriff's Office wrote the girls' mother refused to lower her weapon when police arrived and was shot and killed by a Fulshear officer.
Fort Ben Sheriff Troy Nehls posted an update on Saturday afternoon.
"As everyone is certainly aware, we had a terrible incident last night that involved the deaths of three people," he wrote.
"An unimaginable tragedy that it seems we see too often."
He thanked deputies and detectives for keeping the community safe and offered his prayers to the Sheats family.
The Houston Chronicle reported the girls' father was at home when the shooting took place. He was not injured but was taken to hospital in a distressed state.
"He's going through a very difficult time," Sheriff Nehls said.
In March, Christy wrote on Facebook: "It would be horribly tragic if my ability to protect myself or my family were to be taken away, but that's exactly what Democrats are determined to do by banning semiautomatic weapons."
In January, she shared a post with the following message: "I have 10 guns. Obama wants eight of my guns. How many guns do I have? That's right, I have 10 guns."
The neighbourhood where the shooting took place was described as a "comfortable, middle class subdivision" by the Chronicle.
Christy posted a photo of herself and her two daughters in 2015. She wrote: "Happy Daughter's Day to my two amazing, sweet, kind, beautiful, intelligent girls. I love and treasure you both more than you could ever possibly know."