Authorities didn’t immediately release the identities of the victims in the Oak Hills mobile home park, about 45km west of Fort Worth.
The woman’s sister, who lived nearby, had stopped at the home after the woman failed to show up for work, Parker county sheriff Larry Fowler said.
He said the sister rescued the infant when she realised the baby girl was still alive.
The other children, aged five, three and two, had all been hanged with strips of clothing and sashes, said Mr Fowler.
“It’s terrible, terrible,” he said.
The infant was taken to Cook Children’s Medical Centre in Fort Worth and was in good condition, said Mr Fowler.
Neighbours in the rural community of 1,600 were stunned.
Less than five years earlier, another Hudson Oaks family was torn apart when Dee Etta Perez, 39, shot her three children, aged four, nine and 10, before killing herself.
Mr Fowler said the hangings yesterday also appeared to be murder-suicide, but the investigation was still under way.
The young mother and her girls were last seen alive om Monday evening, he said. She was believed to be separated from her husband, who Mr Fowler said has been notified of the deaths.
“I just got a big kick out of watching the kids play over there on her porch, and today it’s sad, very sad,” said neighbour Joyce Harris.
Texas has seen a disturbing number of child killings by mothers in recent years.
Andrea Yates drowned her five children in the family’s Houston bathtub in 2001. In 2003, Deanna Laney beat her two young sons to death with stones in East Texas, and Lisa Ann Diaz drowned her daughters in a bathtub. Dena Schlosser fatally severed her 10-month-old daughter’s arms with a kitchen knife in 2004.
All four of those women were found innocent by reason of insanity. Yates initially was convicted of capital murder, but it was overturned on appeal.