A woman identified by local media as Megan Huntsman, 39, was arrested early Sunday and booked into the Utah County Jail on murder charges.
Pleasant Grove Police officers on Saturday had "responded to the residence and observed the body of a newborn infant that appeared to be full term," a statement said.
"A search warrant was obtained for the residence and during the execution of the warrant, officers discovered six additional infant bodies. Each infant was found packaged in separate containers."
Police said the investigation revealed that Huntsman had given birth to the infants, and then killed them, over a 10-year period.
The Salt Lake Tribune said the six packaged infant bodies had been placed in cardboard boxes.
Huntsman's ex-husband tipped off police and is believed to be the father of the infants, according to the newspaper.
Huntsman's three daughters still live in the home, owned by the ex-husband's parents, longtime neighbor Sharon Chipman told the Tribune.
Two older girls are aged 18 to 20, while the youngest is about 13.
Chipman said the ex-husband had been cleaning out the garage on Saturday to prepare to move back into the house.