Zuma failed to appear at the inquiry led by Deputy Chief Justice Raymond Zondo in February, after which the inquiry's lawyers approached the constitutional court to seek an order for his imprisonment.
The inquiry is examining allegations of high-level graft during Zuma's period in power from 2009 to 2018. Zuma denies wrongdoing and has so far not cooperated.
"Mr Jacob Gedleyihlekisa Zuma is sentenced to undergo 15 months' imprisonment," a constitutional court judge said, reading out the court's order.
Zuma has to appear before police within five days, the judge added.
A spokesman for Zuma told eNCA television that the former president would issue a statement later, without elaborating.
The allegations against Zuma include that he allowed businessmen close to him - brothers Atul, Ajay and Rajesh Gupta - to plunder state resources and influence policy.
The Guptas, who also deny wrongdoing, left South Africa after Zuma was ousted in a move orchestrated by allies of his successor, President Cyril Ramaphosa.
Ramaphosa has been trying to restore investor confidence in Africa's most industrialised nation. However, he has faced opposition from a faction within the governing African National Congress party that is still loyal to Zuma.