Mr Zuma, who was elected to the presidency in 2009, was due to give evidence to the inquiry on Monday but failed to show up.
The inquiry is now asking the country's constitutional court to impose a jail term on Mr Zuma, who was removed from office by the African National Congress (ANC) in 2018.
Deputy chief justice Raymond Zondo, who is leading the probe, said there was "no valid or sound reason" for Mr Zuma's absence.
"The commission will make an application to the constitutional court, which is the court that made the order that Mr Zuma has defied, and seek an order that Mr Zuma is guilty of contempt of court," Zondo said.
It is up to the constitutional court - the highest in the land - to decide what to do about Mr Zuma, with options including a fine or prison, Mr Zondo added.
Eric Mabuza, one of Mr Zuma's lawyers, declined to comment on the inquiry's call for his client to be locked up.
Mr Zuma denies any wrongdoing but has refused to cooperate with the commission of inquiry.
He was removed from office in a move orchestrated by allies of his successor, Cyril Ramaphosa.
Mr Zuma's lawyers said in a letter to the inquiry on Monday that the 78-year-old would not attend this week when he had been due to give evidence.
"The summons issued for our client to appear on 15 Feb 2021 is irregular," the letter said.
Mr Ramaphosa has been trying to clean up the ANC's image and restore investor confidence in Africa's most industrialised nation since replacing Mr Zuma in 2018.
However, he has faced opposition from an ANC faction still loyal to Zuma.
The allegations against Mr Zuma include that he allowed businessmen close to him - three brothers Atul, Ajay and Rajesh Gupta - to plunder state resources and influence policy.
The Guptas, who deny wrongdoing, left South Africa after Zuma was ousted. Zuma walked out of the inquiry in November without permission.
Its officials then approached the constitutional court to make him reappear and testify.
A lawyer for the inquiry, Paul Pretorius, said Zuma had been implicated by the evidence of at least 40 witnesses.
Speaking near Zuma's Nkandla homestead, Edward Zuma, one of his sons, told reporters there had been a longstanding conspiracy against his father and the inquiry had treated him differently to other witnesses.
Additional reporting by Reuters