A Houston woman and "close friend" of Ms Broussard has been charged with kidnapping and evidence tampering, local police said. She is expected to be charged with murder, news.com.au reports.
The woman, who allegedly pretended to be pregnant, had been plotting to take Ms Broussard's daughter leading up to the child's birth, according to police.
The car in which Ms Boussard's body was found is registered to the woman in custody, police sources told ABC affiliate KEYE. The baby has been placed in Child Protective Services custody, and the body is currently with a medical examiner, the local news outlet reports.
Craig Cummings with the Texas Department of Public Safety earlier told KPRC that investigators were at a home in Jersey Village, northwest of Houston, in connection with the missing mother and her infant.
The FBI also confirmed it was at the site, but a spokeswoman declined to comment further.
Ms Broussard was last known to be alive after returning home from dropping her six-year-old son Silas off at school on December 12. Ms Broussard's fiance Shane Carey told reporters that he last spoke to his fiancee on the day of her disappearance, shortly after 8am. According to Mr Carey, he returned home around 2pm after working all morning and found Ms Broussard's car in the driveway — her purse was still in the car.
Mr Carey said he went inside, found the baby's car seat and Ms Broussard's identification, and thought nothing of it at first, believing she was at a friend's house nearby.
But as hours passed and he was still unable to reach Ms Broussard by phone, Mr Carey said he called her friends, who also hadn't heard from her. That's when he called 911.
He later appeared on morning television where he tearfully appealed to anyone who might have been holding the pair captive to return them home safely.
Ms Broussard's parents, Tammy and David Broussard, also made an emotional plea for her to come home at the time.
"We miss all of them very much, and we want them home. So, anybody who has her, please let them go – just let them go – and it'll be all right," Tammy Broussard said.
"Heidi wouldn't do this, there's no way.
"She loves her son Silas and she would never do this, and she would never take Margot down those stairs without her carrier and have her strapped in and her diaper bag strapped to her back."
Authorities said they are examining security camera footage and Ms Broussard's "digital footprint and any electronic devices" in addition to speaking to neighbours, family, friends, co-workers and past co-workers.
