Investigators believe Megan Huntsman, 39, of Pleasant Grove, gave birth to the babies from 1996 to 2006 and then killed them.
Her estranged husband called police Saturday after he found a dead baby, which "appeared to be a full term" inside the garage, according to a police statement.
"A family member was cleaning out the garage and came across a box that looked suspicious. Upon opening the box they found the infant inside," Capt. Michael Roberts of the Pleasant Grove Police Department told ABC News.
Officers then discovered the bodies of six other infants, stuffed in separate cardboard boxes.
The ex-husband is believed to have fathered all of them, but claims he never knew she was pregnant. DNA samples were taken from the suspect and the husband to determine whether the two are the parents as investigators believe.
Family and neighbors identified the estranged husband as Darren West, a convict who had been in prison.
The former couple owned the house together, but have not lived there since 2011.
Huntsman was booked into the Utah County Jail on six counts of murder.
ABC News and The Associated Press contributed to this report.