"The Constitutional Court... has concluded that the application should be dismissed as it bears no reasonable prospects of success," the court said in the ruling.
The ruling is the last on the matter, as Zuma's application had been previously dismissed by lower courts.
Zuma faces 16 counts of fraud, graft and racketeering over the purchase of fighter jets, patrol boats and equipment while he was vice president in the late 1990s.
In a protracted defense, he had accused prosecutor Billy Downer of bias by leaking confidential medical documents to the media.
The embattled former head of state's long-awaited trial ran into a string of legal delays after starting in May last year.
Earlier this year his defence team secured a postponement on health grounds.
Zuma, 80, was president from 2009 until 2018, when the ruling African National Congress (ANC) forced him out as "state capture" graft scandals besetting his government brewed into a political storm.
Last year he was given a 15-month jail term for contempt of court after refusing to testify before a panel probing financial sleaze and cronyism under his presidency.
That case is separate from the arms scandal, in which he allegedly took bribes from French defense giant Thales, which has also been charged with corruption and money laundering.
Both Thales and Zuma deny any wrongdoing.