At 1602 GMT, the rand traded at 19.3225 against the dollar, 0.16% weaker than its previous close.
The currency also weakened on Thursday and on Friday as the market digested the finance minister's budget speech last week.
In it, the minister said the government would draw down 150 billion rand ($7.76 billion) from contingency reserves at the central bank over the next three years to limit rising debt, but offered little in the way of broad structural reforms.
"The negative mood post the budget speech persists and the risk for further weakness in the short term remains," Andre Cilliers, currency strategist at TreasuryONE, said in a note.
This week, investors will be monitoring trade and budget balance data, producer inflation and private sector credit figures.
On the stock market, the Top-40 and the broader all-share indexes closed around 0.8% lower.
Shares in Sasol fell 2% after the petrochemical firm reported a decline in half-year profit.
South Africa's benchmark 2030 government bond was weaker, with the yield rising 10.5 basis points to 10.240%.
($1 = 19.3213 rand)
(Reporting by Anait Miridzhanian; editing by Susan Fenton and Mark Heinrich)
