She was rushed to the hospital in the early morning hours after being hit by gunfire.
The shooting happened a little after 2 a.m. in the 9000-block of South Oglesby in Calumet Heights.
Police said Garrett was opening the back door of her home to let her grandson inside when multiple shots were fired toward the house. Police said the grandson was not struck.
Garrett's daughter said she was devastated when she got the call Friday morning.
"I immediately broke down and fell to my knees, crying and praying and asking the Lord, you know, 'don't take my mom away from me. Not at this time.' You know what I'm saying? It's not her time to go yet," said Lillie Sharkey.
"This was somebody's grandmother. This was somebody's mother and somebody's auntie. And if they're saying its safe, its not safe," said Andrew Holmes, a community activist. "Look at the amount of people that's being shot and bullets are coming through their homes, and the children that are playing. This is not a joke."
Community activists went door-to-door to ask neighbors to check their surveillance camera since no one is in custody after the shooting.
A $1,000 reward has been offered for more information in the case.
Relatives said Garrett is a great-grandmother and the matriarch of a very large and close family.
She lived in the home on the South Side for more than 30 years and is known to neighbors as "Auntie Georgia" or "Grandma Georgia."
According to relatives, Garrett was conscious and talking late Friday afternoon.
She is expected to survive despite being shot in the arm and underneath her armpit in the chest area.