At 1516 GMT, the rand traded at 19.2350 against the dollar, about 0.5% weaker than its previous close.
The dollar last traded more than 0.6% stronger against a basket of global currencies.
"With the U.S. closed ... most markets were stable, except the rand that fell sharply," said Rand Merchant Bank analysts in a research note.
The rand tumbled after South Africa's struggling state utility Eskom reinstated the worst rolling blackouts on record, which mean up to 12 hours of power cuts for most households per day.
In the second quarter, when Eskom somewhat eased the levels of outages, the country's economy recorded a greater than expected expansion, local data showed on Tuesday.
S&P Global survey showed South Africa's private sector activity grew for the first time in six months in August as improved demand led to firms boosting output.
On the stock market, the Top-40 and the broader all-share indexes closed around 0.5% lower.
South Africa's benchmark 2030 government bond was weaker in afternoon deals, with the yield up 7.5 basis points to 10.410%.
(Reporting by Tannur Anders and Anait Miridzhanian; Editing by Bhargav Acharya and Josie Kao)
