Mo'unga has spent the last three years in Japan and was not picked for the initial tour squad because he was ineligible due to NZR's strict selection policy for overseas-based players.
The 56-cap All Black became eligible after returning home to New Zealand and playing for home province Canterbury.
NZR said Mo'unga was a replacement for centre Billy Proctor, who suffered a shoulder injury and was returning home.
"We really feel for Billy. He has had a great season so this is frustrating for him. It is the harsh reality of our game," All Blacks coach Dave Rennie said in a NZR statement.
"Richie is the obvious choice as a replacement. His job now is to get in and learn our systems, get his head around the detail and earn the right to play."
Mo'unga has already made his mark since returning to New Zealand, scoring the match winner against Auckland before guiding Canterbury to a 19-15 win at Otago to claim the Ranfurly Shield for a record 18th time over the weekend.
Damian McKenzie, one of four flyhalves already in the squad, sprained his ankle in the 54-0 hammering of the Sharks in Durban on Tuesday.
However, Rennie said he would be fit for the first test against the Springboks at Ellis Park on August 22.