The 30-year-old star batsman Azam was dropped following defeat in the first Test against England in October and rested for the ongoing limited-over series against Zimbabwe.
Pakistan will play three Twenty20 internationals in South Africa starting from December 10, followed by three one-day matches and two Tests.
Fast bowler Mohammad Abbas also returns to the Test side after last playing in 2021.
Off-spinner Sajid misses out despite taking 19 wickets in the 2-1 home Test series win over England, with selectors taking into consideration the less spin-friendly pitches in South Africa.
"We have adopted a horses for courses policy to ensure squads are well-balanced and leaving out Sajid was an extremely difficult decision," Aaqib Javed, a senior member of the selection committee, said in a Pakistan Cricket Board statement.
Sajid's spin partner Noman Ali, who took 20 wickets against England, is the only spinner for the Tests in Centurion and Cape Town. The first Test starts on December 26.
Javed said fast bowler Shaheen Shah Afridi has been picked only for the white-ball matches to manage his workload.
Opener Fakhar Zaman is still out because he has yet to regain form and match fitness, said Javed.
Pakistan squads for South Africa tour:
Tests: Shan Masood (captain), Saud Shakeel, Aamer Jamal, Abdullah Shafique, Babar Azam, Haseebullah Khan, Kamran Ghulam, Khurram Shahzad, Mir Hamza, Mohammad Abbas, Mohammad Rizwan, Naseem Shah, Noman Ali, Saim Ayub, Salman Ali Agha
ODIs: Mohammad Rizwan (captain), Abdullah Shafique, Abrar Ahmed, Babar Azam, Haris Rauf, Kamran Ghulam, Mohammad Hasnain, Muhammad Irfan Khan, Naseem Shah, Saim Ayub, Salman Ali Agha, Shaheen Shah Afridi, Sufiyan Muqeem, Tayyab Tahir, Usman Khan
T20Is: Mohammad Rizwan (captain), Abrar Ahmed, Babar Azam, Haris Rauf, Jahandad Khan, Mohammad Abbas Afridi, Mohammad Hasnain, Mohammad Irfan Khan, Omair Bin Yousuf, Saim Ayub, Salman Ali Agha, Shaheen Shah Afridi, Sufiyan Muqeem, Tayyab Tahir, Usman Khan
