The attacker, who helped Chelsea win the Premier League title this season, has been left out of Gernot Rohr's squad as he requires treatment on his toe.
"He has been carrying a toe injury for a while and has surgery scheduled for it," Green told Kwesé ESPN. "The coach has known about it for a while and so have we.
"We decided it was best to let him have his surgery now so he can be ready for the new season."
Without Moses, Trabzonspor midfielder Ogenyi Onazi leads 22 other players named for the matchup against Bafana Bafana.
SC Zamalek defender Maroof Yusuf is a surprise first-time call-up. All invited players are expected in Abuja on Friday 2 June, with the team set to train on Monday 5 June before departing for Uyo on Tuesday.
The Super Eagles play Bafana Bafana at the Godswill Akpabio International Stadium, Uyo in their Group E opener on Saturday 10 June, with the match kicking off at 5pm local time.