Jurgen Klopp, who is a great friend of South Africa and a regular visitor to the country, is Head of Global Soccer for Red Bull and will have played a role in organising the tour.
The German side will have several players missing due to international call-ups for their respective World Cup-bound national teams, but are bringing 16 first-team players and 10 from their academy.
David Raum (Germany), Christoph Baumgartner, Xaver Schlager, Nicolas Seiwald (all Austria), Yan Diomande (Ivory Coast) and Antonio Nusa (Norway) are all concentrating on the global finals.
Maarten Vandevoordt will also link up with Belgium as they prepare for the World Cup, while Andrija Maksimovic and Kosta Nedeljkovic have been called up by Serbia for friendly matches.
Ridle Baku is suffering from illness but may link up with the squad later on.
Leipzig arrive in Johannesburg on Tuesday and will train this week before clashing with Sundowns on Friday night, just after Bafana Bafana take on Nicaragua in a pre-World Cup friendly on the same evening.
“Alongside their football sessions on the pitch, the Red Bulls will also get to know two of South Africa’s most popular sports: cricket and rugby,” a Leipzig statement said.
“Players and staff will gain authentic insights into the country’s sporting culture through dedicated training sessions. Among other activities, several RBL first-team players will take part in a joint session with the Bulls rugby team.”
The team will also attend various other cultural activities before heading back to Germany on Saturday.
Leipzig finished third in the Bundesliga this season and will play in the UEFA Champions League in the next campaign.