It happened around 10:15 p.m. Monday at the Trails of Windfern apartment complex on Windfern near Summer Harvest.
Authorities told ABC13 the man knocked on the woman's door and when she answered, he demanded money and tried to barge in.
She fought with the man, who shot her several times.
The woman called 911 herself after being shot in the hand and chest. She was taken to Ben Taub Hospital and is expected to survive.
Her children, who are both under the age of one, are okay.
"My husband said he saw the guy in the car and said he went in, two gun shots and then left," said Brenda Rivas, who lives next door.
It's unknown at this time if the shooting happened in front of the victim's kids or where they were in the apartment.
ABC13 was there as authorities carried the children out of their home.
Deputies believe the apartment was targeted.
For neighbors, it was a terrifying night that has them worried for their safety.
"It is stuff we have to think about. We have kids here, too, so it makes us want to move, not feeling safe anymore," said Rivas.
Investigators say it doesn't appear that anything was taken, but they are still considering the incident a home invasion.
Deputies do not have a lot on the suspect, only describing him as a black man in his 20s who was wearing a black shirt and sandals.
He left in a black Ford sedan.
A mother was shot — her kids home too — when a man tried to barge into their apartment. Mom is undergoing surgery. Waiting for an update on how she’s doing. https://t.co/4RIBuX8jCg #abc13 pic.twitter.com/KtVWCBMyZ9— Courtney Fischer (@CourtneyABC13) June 11, 2019
Follow Courtney Fischer on Facebook and Twitter.