It will mean a batting order reshuffle for the contest, which starts on Sunday, as Conrad also announced Ryan Rickelton will be the wicketkeeper, which is likely to mean Kyle Verreynne, who has not scored a test fifty in his last 13 innings, will also be dropped though he remains with the squad.
The changes follow South Africa's 214-run defeat in the first test that ended in Durban on Tuesday. Stubbs scored 33 runs in his two innings in the match at Kingsmead.
Breetzke, who has played two previous tests for South Africa, in Bangladesh in late 2024 and Zimbabwe last year and has a first-class average of 37, last played a first-class match in February. But he did score a century in the first One Day International last month when South Africa beat Australia.
"Matt has been part of the squad before and the fact that his ODI form is as hot as it is gave him an inside lane and also, more importantly, the attitude and the character Matt brings, and has, will go a long way," Conrad said.
"With Ricks (Rickelton) taking the gloves, there are obviously decisions to be made over whether he does move down the order or whether he can continue to open the batting and take the gloves, which he has done before," Conrad said.
"We'll have a look at what the conditions are like, but there are a few things to consider before play starts."
That puts Breetzke in contention to open with Aiden Markram while Tony de Zorzi again misses out with the hamstring injury he suffered in last month's ODI series.
Lead pace bowler Kagiso Rabada, who sat out of the first test as a precaution because of long-standing hamstring trouble, is expected to be fit to play.
Squad: Temba Bavuma (captain), Marques Ackerman, David Bedingham, Matthew Breetzke, Corbin Bosch, Gerald Coetzee, Simon Harmer, Marco Jansen, Keshav Maharaj, Aiden Markram, Wiaan Mulder, Senuran Muthusamy, Anrich Nortje, Dane Paterson, Kagiso Rabada, Ryan Rickelton, Kyle Verreynne.