The Giants' five nominees equals the most a club has received in one season, matching Essendon (1993) and Fremantle (1996).
Greene, who was taken with pick No.11 in last year's draft, tallied 31 disposals against the Swans in his side's 94-point loss on Saturday night.
The 18-year-old has been one of GWS's most consistent young guns this season - playing 11 games predominantly in the midfield.
Greene joins teammates Jeremy Cameron, Tomas Bugg, Stephen Coniglio and Dylan Shiel in being nominated for the award that recognises young talent.
"Toby has had an outstanding debut year," GWS coach Kevin Sheedy said.
"He has shown a great ability to not only win the ball but for an 18-year-old he is extremely tough and mature beyond his years."