Michael Blosil apparently jumped from his Los Angeles apartment window Friday night, E! News reported.
The teenager has suffered from depression for some time and left behind a suicide note, the report said.
Osmond released a statement Saturday saying the family was devastated "and in deep shock by the tragic loss of our dear Michael."
Blosil was adopted by Osmond and her former husband, music producer Brian Blosil.
The singer and her brother, Donny, have indefinitely canceled their Las Vegas act, E! reported.
Donny Osmond spoke to "Entertainment Tonight" Saturday, saying: "Please pray for my sister and her family."
Susan Sarandon 'very excited' about daughter's pregnancy
Scarlett Johansson steps out with fiance after pregnancy reveal