A routine examination by army doctors made the transfer necessary, it said without giving further details.
Zuma has been serving a 15-month sentence for contempt of court since the beginning of July. He is due to appear before a commission over corruption charges from his time in office between 2009 and 2018.
However, he did not comply with several summons, which resulted in his imprisonment.
His jailing triggered protests by supporters in which at least 337 people were killed, according to official figures. The security situation stabilized after 25,000 soldiers were mobilized.
The riots also prompted South African President Cyril Ramaphosa to reshuffle his Cabinet on Thursday evening. He also announced a commission of enquiry.
The Ministry of State Security, which was criticized during the wave of violence, will in future be directly attached to the Office of the President. The Defence Ministry is also due to be reorganized. Furthermore, a separate Water Ministry is also to be established.
Zuma is also accused of corruption, money laundering and fraud in connection with an arms deal before he became president. He faces up to 25 years in prison.
His lawyers had recently obtained a three-week postponement of the trial until August 10. Zuma denies the charges.