At 1516 GMT, the rand traded at 19.0200 against the dollar, about 0.75% weaker than its previous close.
The dollar index was last trading up about 0.18% against a basket of currencies.
Iran launched more than 300 drones and missiles at Israel over the weekend in retaliation for what it said was an Israeli airstrike on its Damascus consulate on April 1.
Rising insecurity in the Middle East tends to spur demand for the safe-haven greenback. The dollar was also boosted by U.S. retail sales figures which increased in March.
"Developments in the Middle East over the next few days are likely to remain the main focus and driver for currency moves and keep the dollar on the front foot," said Andre Cilliers, currency strategist at TreasuryONE.
South African investors will also be looking at March inflation and February retail sales figures later in the week.
On the stock market, the Top-40 index closed 1.24% lower, while the broader all-share index was down 1.05%.
South Africa's benchmark 2030 government bond was weaker, with the yield up 4 basis point to 10.785%.
(Reporting by Bhargav Acharya and Nellie Peyton; Editing by Mark Heinrich and David Holmes)
