"We will propose a new law to stop excessive salaries in these public entities," Mboweni said.
He proposed a 160-billion-rand ($10.5-billion, 9.67-billion-euro) cut in wages over the next three years, which translates to around a nine percent reduction in the first year.
Weak growth, deteriorating public finances including a swollen budget deficit, crippling power cuts and soaring unemployment combine to cloud South Africa's economic outlook.
Despite efforts to rein in state expenditure, Mboweni also pledged 60 billion rand ($3.9 billion) to South Africa's struggling power utility Eskom and cash-strapped flag carrier South African Airways (SAA).
"Government will do whatever it takes to ensure a stable electricity supply," said Mboweni.
A sovereign wealth fund will be created with a target capital amount of around 30 billion rand ($2 billion), he added. "There's lots of cleaning-up things we can do," Mboweni told reporters in a pre-budget news conference. "But my experience now is (that) sometimes trying to get rid of very simple wastage things in the state system is like going to the dentist to get your teeth taken out without anaesthetic," he said.
According to budget documents, the country's economy grew by only around 0.3 percent in 2019, and is expected to grow by a dismal 0.9 percent in 2020. The budget deficit currently stands at 6.3 percent of gross domestic product (GDP).
Other cost-saving measures will include requiring all government officials to travel economy class on domestic flights.
Additionally, the foreign ministry will close and merge some overseas diplomatic missions and reduce their staffs. Unemployment is creeping towards 30 percent, the highest level in more than a decade. South African political analyst Daniel Sile said Mboweni had presented a "credible yet politically risky budget".
"Cuts to the state wage bill (are) likely to cause tension with the unions but (are) essential to restoring fiscal stability," Sile tweeted after the speech.
South Africa's main opposition party, the Democratic Alliance (DA), blasted the government for "wasting money" on state-owned enterprises. "It is outrageous that funds desperately needed to stimulate the economy and the creation of jobs is to poured into the SAA vanity project," said the DA in a statement.
Mboweni's budget will be under the scrutiny of international ratings agency Moody's, the only major assessor that still considers South African debt to be investment grade.
Fitch and S&P downgraded South Africa's credit rating to junk status in 2017.
"We are on the verge of a Moody's rating downgrade, and if we don't stabilise the deficit and get spending under control, they will downgrade us," Els said.
Losing its last investment grade rating could spark an exodus from South Africa's bond markets and pile pressure on the rand.
The country's lacklustre economic performance is largely a result of domestic issues.
Repeated bailouts to state-owned entities over the past decade - most notably to Eskom and flag-carrier South African Airways - have drained state coffers.
In the past five years, South Africa has posted its weakest growth rates - never exceeding 1.3 percent and in some years falling below one percent.
The World Bank recently warned that South Africa was on a precipice, and cut its economic growth forecast to below one percent in 2020 as well due to electricity supply concerns.
"The budget confirms the extent to which the SA economy still finds itself in a bad space," said South African economist Ray Parsons.
"What clearly again shines through the fiscal gloom of recent years is the need for... boosting investor confidence and turning the economy around."