Police did not identify the suspect but said the person's bail is $600,000 and they now remain in custody.
A baby girl was also found alive and healthy at the home, the statement said.
One person has been arrested and faces two charges of kidnapping and one charge of tampering with a corpse, Manley said.
The woman's fiancé, Shane Carey, reported her missing.
Tammy Broussard told NBC News that she was told by police that the body is likely that of her daughter, Heidi Broussard, and that the body was found in the trunk of a auto at the home in Jersey Village about 130 miles (209 kilometers) southeast of Austin.
The body and the baby were found when a dozen officers from the Texas Rangers, Texas Department of Public Safety, FBI and Austin Police Department converged on the house in northwest Harris County Thursday evening, according to ABC's Houston station, KTRK.
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Police are asking people to share their tips with the Austin Police Department.
Broussard, 33, and her infant daughter, Margot Carey, were last seen dropping off a child at Austin's Cowan Elementary School on the morning of December 12, according to the Austin Police Department.
The investigation is ongoing, they said. She is in the custody of Texas Child Protective Services and DNA testing will determine whether the baby is Broussard's daughter, Margot Carey.
Investigators believe Broussard and her child returned home to their apartment complex after they left the school. "It feels like we could do more".
Authorities also told Tammy that her 3-week-old granddaughter, Margot Carey, was found safe inside a home in Jersey Village. That's when he called 911. The couple had been together for almost 10 years, Carey said.
Austin police established a tip line for the case.