De Kock suffered torn ligaments in his left ankle ahead of the third day's play in the first Test at Centurion last week and remains a doubt for the Cricket World Cup in February.
Rossouw, who has had a memorable year on the international scene having made his one-day and Twenty20 debuts since August, could add a five-day cap later this week.
Cricket South Africa (CSA) confirmed the 25-year-old would replace De Kock in the Test squad for the final two matches of the series, with the Proteas already 1-0 ahead.
"Rilee has been knocking on the door for some time," said CSA selection convener Andrew Hudson.
"He and Temba Bavuma shared a partnership of 343 at a run rate of almost four to the over in the recent winning series for South Africa A against Australia A.
"The fact that he has also recently represented the Proteas in both the limited-overs formats means that he will integrate easily into the Proteas squad system."
However, Rossouw has been troubled by a finger injury in recent weeks so he may have to wait for his chance, with Bavuma another option for Hashim Amla's side.
The second Test begins on Friday at St George's Park in Port Elizabeth, before the final encounter in Cape Town in the new year.