The commission's chairman announced a two-week postponement after a brief first hearing -- to allow the replacement of judges and the classification of secret military documents.
The inquiry will resume on August 19.
Zuma was expected to appear before the commission probing graft allegations against him and several top government officials.
The commission is investigating kickbacks in a $3 billion weapons deal made in 1999 that has dogged Zuma and his ruling ANC for a decade.
More From This Section
The head judge Francis Legodi quit last week, citing "personal reasons" and a legal researcher also resigned, saying commission had "incompetent administration."
Security was boosted around the Pretoria Council Chamber where the hearing took place, with police vehicles and fire trucks stationed outside.
With less than a year before elections in South Africa, the saga risks undermining the credibility of both Zuma and the African National Congress with voters.