The baby was listed in critical condition and the mother in stable condition Thursday evening.
Each was identified only by the last name, Hawkins.
More than 100 followers of House of Yahweh leader Yisrayl Hawkins have legally changed their last name to Hawkins in the last couple of years.
A dispatcher at the Callahan County Sheriff's Office said a call came at 4:26 p.m. and two ambulances were dispatched, one for the baby and one for the mother. Citizens EMS of Clyde transported the baby and Rural/Metro of Abilene took the mother.
Three deputies also went to the site. One deputy said a midwife was with the mother when help arrived and that the mother appeared to be in good condition.
The dispatcher, who asked not to be identified, said the woman who called was phoning from a house next to the one where the baby was born.
"The lady couldn't give a house number to save her neck," the dispatcher said.
The caller had to go back and forth between houses, making the dispatcher's job more difficult.
"I couldn't even give her instructions on what to do," she said.
The ambulance drivers and deputies finally were able to locate the mobile home located outside the compound grounds, the dispatcher said.
Even though the woman who called was unable to give good directions, she did remain calm, the dispatcher said.
"She was very concerned, but calm," she said.