At 1518 GMT, the rand traded at 13.9300 versus the U.S. currency, 0.3 percent weaker than its previous close.
Similar falls were seen in other emerging market currencies like the Russian rouble and Turkish lira as the dollar index was more than 0.2 percent stronger.
"Appetite for the rand and many other emerging markets has been impacted by a stabilizing dollar," said Hussein Sayed, chief market strategist at forex broker FXTM.
After a torrid 2018 the rand enjoyed a strong start to this year, helped by dovish comments by U.S. Federal Reserve policymakers which hurt the dollar.
Despite Tuesday's decline, it is still up more than 2 percent against the dollar in 2019.
On the bourse, the benchmark JSE Top-40 index ended 0.5 percent higher at 46,116 while the broader All-share index gained 0.6 percent to 52,165.
In fixed income, government bonds also fell, with the yield on the 2026 bond up 4 basis points to 8.810 percent.
The government sold 2.85 billion rand ($204 million) of bonds on Tuesday at lower yields than previously.
($1 = 14.0023 rand)
(Reporting by Alexander Winning and Tiisetso Motsoeneng, editing by Ed Osmond)
